Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T13:36:35.378Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 February 2016

Uwe Franz  and
Nicolas Privault
Uwe Franz
Affiliation:
Université de Franche-Comté
Nicolas Privault
Affiliation:
Nanyang Technological University, Singapore
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Probability on Real Lie Algebras , pp. 271 - 278
Publisher: Cambridge University Press
Print publication year: 2016

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] L, Accardi, U., Franz, and M., Skeide.Renormalized squares of white noise and other non-Gaussian noises as Lévy processes on real Lie algebras. Comm. Math. Phys., 228(1):123–150, 2002. (Cited on pages xvii, 17, 38, 40, 96, 132, 147, and 187).Google Scholar
[2] L., Accardi, M., Schürmann, and W.v., Waldenfels.Quantum independent increment processes on superalgebras. Math. Z., 198:451–477, 1988. (Cited on pages xvii and 131).
[3] G.S., Agarwal.|Quantum Optics. Cambridge University Press, Cambridge, 2013. (Cited on page 130).Google Scholar
[4] N.I., Akhiezer.The Classical Moment Problem and Some Related Questions in Analysis. Translated by N., Kemmer.Hafner Publishing Co., New York, 1965. (Cited on page 54).Google Scholar
[5] N.I., Akhiezer and I.M., Glazman.Theory of Linear Operators in Hilbert Space. Dover Publications Inc., New York, 1993. (Cited on page 243).Google Scholar
[6] S., Albeverio, Yu. G., Kondratiev, and M., Röckner.Analysis and geometry on configuration spaces.J. Funct. Anal., 154(2):444–500, 1998. (Cited on page 162).Google Scholar
[7] S.T., Ali, N.M., Atakishiyev, S.M., Chumakov, and K.B., Wolf.The Wigner function for general Lie groups and the wavelet transform.Ann. Henri Poincaré, 1(4):685–714, 2000. (Cited on pages xvi, xvii, 114, 115, 118, 120, 122, 123, 124, and 191).Google Scholar
[8] S.T., Ali, H., Führ, and A.E., Krasowska.Plancherel inversion as unified approach to wavelet transforms and Wigner functions. Ann. Henri Poincaré, 4(6):1015– 1050, 2003. (Cited on pages xvi and 124).Google Scholar
[9] G.W., Anderson, A., Guionnet, and O., Zeitouni.An Introduction to Random Matrices. Cambridge: Cambridge University Press, 2010. (Cited on page 88).Google Scholar
[10] U., Franz and A., Skalski. Noncommutative Mathematics for Quantum Systems. To appear in the Cambridge IISc Series, 2015. D. Applebaum, Probability on compact Lie groups, volume 70 of Probability Theory and Stochastic Modelling, Springer, 2014” after 45th entry (Cited on pages xvi and 99).
[11] M., Anshelevich. Orthogonal polynomials and counting permutations. www .math.tamu.edu/~manshel/papers/OP-counting-permutations.pdf, 2014. (Cited on page 233).
[12] N.M., Atakishiyev, S.M., Chumakov, and K.B., Wolf.Wigner distribution function for finite systems. J. Math. Phys., 39(12):6247–6261, 1998. (Cited on page 125).Google Scholar
[13] V.P., Belavkin.A quantum nonadapted Itô formula and stochastic analysis in Fock scale. J. Funct. Anal., 102:414–447, 1991. (Cited on pages 88, 190, 212, and 213).Google Scholar
[14] V.P., Belavkin.A quantum nonadapted stochastic calculus and nonstationary evolution in Fock scale. In Quantum Probability and Related Topics VI, pages 137–179. World Sci. Publishing, River Edge, NJ, 1991. (Cited on pages 88, 190, 212, and 213).Google Scholar
[15] V.P., Belavkin.On quantum Itô algebras. Math. Phys. Lett., 7:1–16, 1998. (Cited on page 88).Google Scholar
[16] C., Berg, J.P.R., Christensen, and P., Ressel.Harmonic Analysis on Semigroups, volume 100 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1984. Theory of positive definite and related functions. (Cited on page 88).Google Scholar
[17] Ph., Biane.Calcul stochastique non-commutatif. In Ecole d'Eté de Probabilités de Saint-Flour, volume 1608 of Lecture Notes in Mathematics.Springer-Verlag, Berlin, 1993. (Cited on pages 7, 88, 211, and 264).Google Scholar
[18] Ph., Biane.Quantum Markov processes and group representations. In Quantum Probability Communications, QP-PQ, X, pages 53–72. World Sci. Publishing, River Edge, NJ, 1998. (Cited on pages xvii, 132, and 189).Google Scholar
[19] Ph., Biane and R., Speicher.Stochastic calculus with respect to free Brownian motion and analysis on Wigner space. Probab. Theory Related Fields, 112(3):373–409, 1998. (Cited on pages 88 and 216).Google Scholar
[20] L.C., Biedenharn and J.D., Louck.Angular Momentum in Quantum Physics. Theory and Application. With a foreword by P.A. Carruthers. Cambridge: Cambridge University Press, reprint of the 1981 hardback edition edition, 2009. (Cited on page 72).Google Scholar
[21] L.C., Biedenharn and J.D., Louck.The Racah-Wigner Algebra in Quantum Theory. With a foreword by P.A. Carruthers. Introduction by G.W. Mackey.Cambridge: Cambridge University Press, reprint of the 1984 hardback ed. edition, 2009. (Cited on page 72).Google Scholar
[22] J.-M., Bismut.Martingales, the Malliavin calculus and hypoellipticity under general Hörmander's conditions. Z. Wahrsch. Verw. Gebiete, 56(4):469–505, 1981. (Cited on pages xvii and 189).Google Scholar
[23] F., Bornemann.Teacher's corner - kurze Beweise mit langer Wirkung. Mitteilungen der Deutschen Mathematiker-Vereinigung, 10:55–55, July 2002. (Cited on page 258).Google Scholar
[24] N., Bouleau, editor. Dialogues autour de la création mathématique.Association Laplace-Gauss, Paris, 1997.Google Scholar
[25] T., Carleman.Les Fonctions Quasi Analytiques. Paris: Gauthier-Villars, Éditeur, Paris, 1926. (Cited on page 221).Google Scholar
[26] M.H., Chang.Quantum Stochastics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2015. (Cited on pages xviii and 88).Google Scholar
[27] T.S., Chihara.An Introduction to Orthogonal Polynomials. Gordon and Breach Science Publishers, New York-London-Paris, 1978. Mathematics and Its Applications, Vol. 13. (Cited on page 233).Google Scholar
[28] S.M., Chumakov, A.B., Klimov, and K.B., Wolf.Connection between two wigner functions for spin systems. Physical Review A, 61(3):034101, 2000. (Cited on page 125).Google Scholar
[29] L., Cohen.Time-Frequency Analysis: Theory and Applications. Prentice-Hall, New Jersey, 1995. (Cited on pages xvii and 130).Google Scholar
[30] M., Cook.Mathematicians: An Outer View of the Inner World. Princeton University Press, USA, 2009. With an introduction by R. C. Gunning.Google Scholar
[31] D., Dacunha-Castelle and M., Duflo.Probability and Statistics. Vol. I. Springer- Verlag, New York, 1986. (Cited on page xvii).Google Scholar
[32] D., Dacunha-Castelle and M., Duflo.Probability and Statistics. Vol. II. Springer- Verlag, New York, 1986. (Cited on page xvii).Google Scholar
[33] P.A.M., Dirac.The Principles of Quantum Mechanics. Oxford, at the Clarendon Press, 1947. 3rd ed.Google Scholar
[34] M., Duflo and C.C., Moore.On the regular representation of a nonunimodular locally compact group. J. Funct. Anal., 21(2):209–243, 1976. (Cited on page 114).Google Scholar
[35] A., Erdélyi, W., Magnus, F., Oberhettinger, and F.G., Tricomi.Higher Transcendental Functions, volume 2. McGraw Hill, New York, 1953. (Cited on page 264).Google Scholar
[36] P., Feinsilver and J., Kocik.Krawtchouk matrices from classical and quantum random walks. In Algebraic methods in statistics and probability. AMS special session on algebraic methods in statistics, Univ. of Notre Dame, IN, USA, April 8–9, 2000, pages 83–96. Providence, RI: AMS, American Mathematical Society, 2001. (Cited on page 72).Google Scholar
[37] P., Feinsilver and R., Schott.Krawtchouk polynomials and finite probability theory. In Probability Measures on groups X. Proceedings of the Tenth Oberwolfach conference, held November 4-10, 1990 in Oberwolfach, Germany, pages 129–135. New York, NY: Plenum Publishing Corporation, 1991. (Cited on page 72).Google Scholar
[38] P., Feinsilver and R., Schott.Algebraic structures and operator calculus, Vol. I: Representations and Probability Theory, volume 241 of Mathematics and Its Applications. Kluwer Academic Publishers Group, Dordrecht, 1993. (Cited on pages xviii, 92, 94, and 95).
[39] P., Feinsilver and R., Schott.Algebraic structures and operator calculus. Vol. II, volume 292 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht, 1994. Special functions and computer science. (Cited on page xv).Google Scholar
[40] P., Feinsilver and R., Schott.Algebraic structures and operator calculus. Vol. III, volume 347 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht, 1996. Representations of Lie groups. (Cited on page 99).Google Scholar
[41] R.P., Feynman, R., Leighton, and M., Sands.The Feynman Lectures on Physics. Vols. 1-3. Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1964- 1966. www.feynmanlectures.info (Cited on pages 70 and 72).Google Scholar
[42] U., Franz. Classical Markov processes from quantum Lévy processes. Inf. Dim. Anal., Quantum Prob., and Rel. Topics, 2(1):105–129, 1999. (Cited on pages xvii and 132).Google Scholar
[43] U., Franz, R., Léandre, and R., Schott.Malliavin calculus for quantum stochastic processes. C. R. Acad. Sci. Paris Sér. I Math., 328(11):1061–1066, 1999. (Cited on page xviii).Google Scholar
[44] U., Franz, R., Léandre, and R., Schott.Malliavin calculus and Skorohod integration for quantum stochastic processes. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 4(1):11–38, 2001. (Cited on page xviii).Google Scholar
[45] U., Franz and R., Schott.Stochastic Processes and Operator Calculus on Quantum Groups. Kluwer Academic Publishers G roup, Dordrecht, 1999. (Cited on pages 139 and 147).Google Scholar
[46] U., Franz and N., Privault.Quasi-invariance formulas for components of quantum Lévy processes. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 7(1):131– 145, 2004. (Cited on page 16).Google Scholar
[47] C.W., Gardiner and P., Zoller.Quantum Noise. Springer Series in Synergetics. Springer-Verlag, Berlin, second edition, 2000. A handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics. (Cited on pages xvii and 131).Google Scholar
[48] C., Gerry and P., Knight.Introductory Quantum Optics. Cambridge University Press, Cambridge, 2004. (Cited on page 128).Google Scholar
[49] L., Gross.Abstract Wiener spaces. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, 1967. Univ. of California Press. (Cited on page 173).Google Scholar
[50] A., Guichardet.Symmetric Hilbert spaces and related topics, volume 261 of Lecture Notes in Mathematics. Springer Verlag, Berlin, Heidelberg, New York, 1972. (Cited on page 88).Google Scholar
[51] A., Guichardet.Cohomologie des groupes topologiques et des algèbres de Lie., volume 2 of Textes Mathematiques. CEDIC/Fernand Nathan, Paris, 1980. (Cited on pages 147 and 148).Google Scholar
[52] T., Hida.Brownian Motion. Springer Verlag, Berlin 1981. (Cited on page 158).Google Scholar
[53] A.S., Holevo.Statistical structure of quantum theory, volume 67 of Lecture Notes in Physics. Monographs. Springer-Verlag, Berlin, 2001. (Cited on pages xvii and 131).Google Scholar
[54] R.L., Hudson and K.R., Parthasarathy.Quantum Itô's formula and stochastic evolutions. Comm. Math. Phys., 93(3):301–323, 1984. (Cited on pages 190, 212, 214, and 215).Google Scholar
[55] C.J., Isham.Lectures on quantum theory. Imperial College Press, London, 1995. Mathematical and structural foundations. (Cited on page xviii).Google Scholar
[56] Y., Ishikawa.Stochastic Calculus of Variations for Jump Processes. de Gruyter, Berlin, 2013. (Cited on page xviii).Google Scholar
[57] L., Isserlis.On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables. Biometrika, 12(1-2): 134–139, 1918. (Cited on page 240).Google Scholar
[58] S., Janson.Gaussian Hilbert spaces, volume 129 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1997. (Cited on pages 155 and 211).Google Scholar
[59] U.C., Ji and N., Obata.Annihilation-derivative, creation-derivative and representation of quantum martingales. Commun. Math. Phys., 286(2):751–775, 2009. (Cited on page 216).Google Scholar
[60] U.C., Ji and N., Obata.Calculating normal-ordered forms in Fock space by quantum white noise derivatives. Interdiscip. Inf. Sci., 19(2):201–211, 2013. (Cited on page 216).Google Scholar
[61] J.R., Johansson, P.D., Nation, and F., Nori.Qutip: An open-source python framework for the dynamics of open quantum systems. Computer Physics Communications, 183(8):1760–1772, 2012. (Cited on page 113).Google Scholar
[62] J.R., Johansson, P.D., Nation, and F., Nori. Qutip 2: A python framework for the dynamics of open quantum systems. Computer Physics Communications, 184(4):1234–1240, 2013. (Cited on page 113).Google Scholar
[63] R., Koekoek and R.F., Swarttouw. The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. Delft University of Technology, Report 98–17, 1998. (Cited on pages 40, 41, 237, and 238).Google Scholar
[64] A., Korzeniowski and D., Stroock. An example in the theory of hypercontractive semigroups. Proc. Amer. Math. Soc., 94:87–90, 1985. (Cited on pages 18 and 26).Google Scholar
[65] P.S. de, Laplace. Théorie Analytique des Probabilités. V. Courcier, Imprimeur, 57 Quai des Augustins, Paris, 1814.Google Scholar
[66] M., Ledoux.Concentration of measure and logarithmic Sobolev inequalities. In Séminaire de Probabilités XXXIII, volume 1709 of Lecture Notes in Math., pages 120–216. Springer, Berlin, 1999. (Cited on page 18).Google Scholar
[67] V.P., Leonov and A.N., Shiryaev. On a method of calculation of semi-invariants. Theory Probab. Appl., 4:319–329, 1959. (Cited on pages 239 and 240).Google Scholar
[68] J.M., Lindsay.Quantum and non-causal stochastic calculus. Probab. Theory Related Fields, 97:65–80, 1993. (Cited on pages 88, 190, 212, and 213).Google Scholar
[69] J.M., Lindsay. Integral-sum kernel operators. In Quantum Probability Communications (Grenoble, 1998), volume XII, page 121. World Scientific, Singapore, 2003. (Cited on page 88).Google Scholar
[70] J.M., Lindsay.Quantum stochastic analysis – an introduction. In Quantum independent increment processes. I, volume 1865 of Lecture Notes in Math., pages 181–271. Springer, Berlin, 2005. (Cited on page 88).Google Scholar
[71] E., Lukacs. Applications of Faà di Bruno's formula in mathematical statistics. Am. Math. Mon., 62:340–348, 1955. (Cited on pages 239 and 240).Google Scholar
[72] E., Lukacs.Characteristic Functions. Hafner Publishing Co., New York, 1970. Second edition, revised and enlarged. (Cited on pages 239 and 240).Google Scholar
[73] H., Maassen.Quantum markov processes on fock space described by integral kernels. In Quantum probability and applications II (Heidelberg 1984), volume 1136 of Lecture Notes in Math., pages 361–374. Springer, Berlin, 1985. (Cited on page 88).Google Scholar
[74] T., Mai, R., Speicher, and M., Weber. Absence of algebraic relations and of zero divisors under the assumption of full non-microstates free entropy dimension. Preprint arXiv:1502.06357, 2015. (Cited on page 216).
[75] P., Malliavin. Stochastic calculus of variations and hypoelliptic operators. In Intern. Symp. SDE. Kyoto, pages 195–253, Tokyo, 1976. Kinokumiya. (Cited on pages xiii, xvii, and 173).Google Scholar
[76] P., Malliavin.Stochastic analysis, volume 313 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, 1997. (Cited on page 155).Google Scholar
[77] P., Malliavin.Stochastic analysis, volume 313 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, 1997. (Cited on page 169).Google Scholar
[78] S., Mazur and W., Orlicz.Grundlegende Eigenschaften der polynomischen Operationen. I. Stud. Math., 5:50–68, 1934. (Cited on page 259).Google Scholar
[79] P.A., Meyer.Quantum probability for probabilists, volume 1538 of Lecture Notes in Math. Springer-Verlag, Berlin, 2nd edition, 1995. (Cited on pages 7, 88, 135, 147, 186, and 211).Google Scholar
[80] P.A., Meyer.Quantum probability seen by a classical probabilist. In Probability towards 2000 (New York, 1995), volume 128 of Lecture Notes in Statist., pages 235–248. Springer, New York, 1998. (Cited on page xvi).Google Scholar
[81] A., Nica and R., Speicher. Lectures on the combinatorics of free probability, volume 335 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2006. (Cited on page 88).Google Scholar
[82] M.A., Nielsen and I.L., Chuang. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2000. (Cited on page 70).Google Scholar
[83] D., Nualart. Analysis on Wiener space and anticipating stochastic calculus. In Ecole d’été de Probabilités de Saint-Flour XXV, volume 1690 of Lecture Notes in Mathematics, pages 123–227. Springer-Verlag, Berlin, 1998. (Cited on page 155).Google Scholar
[84] D., Nualart. The Malliavin calculus and related topics. Probability and its Applications. Springer-Verlag, Berlin, second edition, 2006. (Cited on pages xvii, 155, and 173).Google Scholar
[85] H., Oehlmann. Analyse temps-fréquence de signaux vibratoires de boîtes de vitesses. PhD thesis, Université Henri Poincaré Nancy I, 1996. (Cited on page 130).
[86] H., Osswald. Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion, volume 191 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 2012. (Cited on pages xviii and 169).Google Scholar
[87] K.R., Parthasarathy. An Introduction to Quantum Stochastic Calculus. Birkäuser, 1992. (Cited on pages xv, 7, 47, 48, 82, 86, 88, 135, 186, 208, 212, 214, and 225).Google Scholar
[88] K.R., Parthasarathy. Lectures on quantum computation, quantum errorcorrecting codes and information theory. Tata Institute of Fundamental Research, Mumbai, 2003. Notes by Amitava Bhattacharyya. (Cited on page 72).Google Scholar
[89] G.|Peccati and M., Taqqu.Wiener Chaos: Moments, Cumulants and Diagrams: A survey with Computer Implementation. Bocconi and Springer Series. Springer, Milan, 2011. (Cited on page 239).Google Scholar
[90] J., Pitman. Combinatorial stochastic processes, volume 1875 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2006. Lectures from the 32nd Summer School on Probability Theory held in Saint-Flour, July 7–24, 2002. (Cited on page 239).Google Scholar
[91] N., Privault. Inégalités de Meyer sur l'espace de Poisson. C. R. Acad. Sci. Paris Sér. I Math., 318:559–562, 1994. (Cited on page 18).Google Scholar
[92] N., Privault.A transfer principle from Wiener to Poisson space and applications. J. Funct. Anal., 132:335–360, 1995. (Cited on page 26).Google Scholar
[93] N., Privault.A different quantum stochastic calculus for the Poisson process. Probab. Theory Related Fields, 105:255–278, 1996. (Cited on pages 16 and 265).Google Scholar
[94] N., Privault.Girsanov theorem for anticipative shifts on Poisson space. Probab. Theory Related Fields, 104:61–76, 1996. (Cited on page 173).Google Scholar
[95] N., Privault.Une nouvelle représentation non-commutative du mouvement brownien et du processus de Poisson. C. R. Acad. Sci. Paris Sér. I Math., 322:959–964, 1996. (Cited on page 16).Google Scholar
[96] N., Privault. Absolute continuity in infinite dimensions and anticipating stochastic calculus. Potential Analysis, 8(4):325–343, 1998. (Cited on page 173).Google Scholar
[97] N., Privault. Splitting of Poisson noise and Lévy processes on real Lie algebras. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 5(1):21–40, 2002. (Cited on pages 16 and 265).Google Scholar
[98] N., Privault.Stochastic analysis in discrete and continuous settings with normal martingales, volume 1982 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2009. (Cited on pages 149, 155, and 174).Google Scholar
[99] N., Privault.Generalized Bell polynomials and the combinatorics of Poisson central moments. Electron. J. Combin., 18(1):Research Paper 54, 10, 2011. (Cited on page 241).Google Scholar
[100] N., Privault and W., Schoutens. Discrete chaotic calculus and covariance identities. Stochastics Stochastics Rep., 72(3-4):289–315, 2002. (Cited on page 72).Google Scholar
[101] L., Pukanszky.Leçon sur les repréntations des groupes. Dunod, Paris, 1967. (Cited on page 142).Google Scholar
[102] L., Pukanszky. Unitary representations of solvable Lie groups. Ann. scient. Éc. Norm. Sup., 4:457–608, 1971. (Cited on page 142).Google Scholar
[103] R., Ramer. On nonlinear transformations of Gaussian measures. J. Funct. Anal., 15:166–187, 1974. (Cited on page 173).Google Scholar
[104] S., Sakai.C*-Algebras and W*-Algebras. Springer-Verlag, New York-Heidelberg, 1971. (Cited on page 179).Google Scholar
[105] M., Schürmann.The Azéma martingales as components of quantum independent increment processes. In J., Azéma, P.A., Meyer, and M., Yor, editors, Séminaire de Probabilités XXV, volume 1485 of Lecture Notes in Math. Springer-Verlag, Berlin, 1991. (Cited on pages xvii and 132).Google Scholar
[106] M., Schürmann.White Noise on Bialgebras. Springer-Verlag, Berlin, 1993. (Cited on pages xvii, 131, 134, 136, 147, and 179).Google Scholar
[107] I., higekawa. Derivatives of Wiener functionals and absolute continuity of induced measures. J. Math. Kyoto Univ., 20(2):263–289, 1980. (Cited on page 173).Google Scholar
[108] K.B., Sinha and D., Goswami. Quantum stochastic processes and noncommutative geometry, volume 169 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 2007. (Cited on page xviii).Google Scholar
[109] R. F., Streater. Classical and quantum probability. J. Math. Phys., 41(6):3556– 3603, 2000. (Cited on pages xvii and 147).Google Scholar
[110] T.N., Thiele. On semi invariants in the theory of observations. Kjöbenhavn Overs., pages 135–141, 1899. (Cited on page 239).Google Scholar
[111] N., Tsilevich, A.M., Vershik, and M., Yor. Distinguished properties of the gamma process and related topics. math.PR/0005287, 2000. (Cited on pages xvii, 180, and 189).
[112] N., Tsilevich, A.M., Vershik, and M., Yor. An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process. J. Funct. Anal., 185(1):274–296, 2001. (Cited on pages xvii, 180, and 189).Google Scholar
[113] A.S., ü stünel. An introduction to analysis on Wiener space, volume 1610 of Lecture Notes in Mathematics. Springer Verlag, Berlin, 1995. (Cited on page 155).Google Scholar
[114] A.M., Vershik, I.M., Gelfand, and M.I., Graev. A commutative model of the group of currents SL(2,R)X connected with a unipotent subgroup. Funct. Anal. Appl., 17(2):137–139, 1983. (Cited on pages xvii and 189).Google Scholar
[115] N.J., Vilenkin and A.U., Klimyk. Representation of Lie groups and special functions. Vol. 1, volume 72 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1991. (Cited on page 99).Google Scholar
[116] N.J., Vilenkin and A.U., Klimyk. Representation of Lie groups and special functions. Vol. 3, volume 75 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1992. (Cited on page 99).Google Scholar
[117] N.J., Vilenkin and A.U., Klimyk. Representation of Lie groups and special functions. Vol. 2, volume 74 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1993. (Cited on page 99).Google Scholar
[118] N.J., Vilenkin and A.U., Klimyk.Representation of Lie groups and special functions, volume 316 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht, 1995. (Cited on page 99).Google Scholar
[119] J., Ville. Théorie et applications de la notion de signal analytique. Câbles et Transmission, 2:61–74, 1948. (Cited on page 130).Google Scholar
[120] D., Voiculescu. Lectures on free probability theory. In Lectures on probability theory and statistics (Saint-Flour, 1998), volume 1738 of Lecture Notes in Math., pages 279–349. Berlin: Springer, 2000. (Cited on page 88).Google Scholar
[121] D., Voiculescu, K., Dykema, and A., Nica. Free random variables. A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups, volume 1 of CRM Monograph Series. American Mathematical Society, Providence, RI, 1992. (Cited on page 88).Google Scholar
[122] W. von, Waldenfels. Itô solution of the linear quantum stochastic differential equation describing light emission and absorption. In Quantum probability and applications to the quantum theory of irreversible processes, Proc. int. Workshop, Villa Mondragone/Italy 1982, volume 1055 of Lecture Notes in Math., pages 384–411. Springer-Verlag, Berlin, 1984. (Cited on pages xvii and 131).Google Scholar
[123] W. von, Waldenfels. A measure theoretical approach to quantum stochastic processes, volume 878 of Lecture Notes in Physics. Monographs. Springer- Verlag, Berlin, 2014. (Cited on page xviii).Google Scholar
[124] E.P., Wigner. On the quantum correction for thermodynamic equilibrium. Phys. Rev., 40:749–759, 1932. (Cited on page xvi).Google Scholar
[125] M.W., Wong. Weyl Transforms. Universitext. Springer-Verlag, Berlin, 1998. (Cited on page 108).Google Scholar
[126] L.M., Wu. L1 and modified logarithmic Sobolev inequalities and deviation inequalities for Poisson point processes. Preprint, 1998. (Cited on page 167).

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Uwe Franz, Université de Franche-Comté, Nicolas Privault, Nanyang Technological University, Singapore
  • Book: Probability on Real Lie Algebras
  • Online publication: 05 February 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316415054.017
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Uwe Franz, Université de Franche-Comté, Nicolas Privault, Nanyang Technological University, Singapore
  • Book: Probability on Real Lie Algebras
  • Online publication: 05 February 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316415054.017
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Uwe Franz, Université de Franche-Comté, Nicolas Privault, Nanyang Technological University, Singapore
  • Book: Probability on Real Lie Algebras
  • Online publication: 05 February 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316415054.017
Available formats
×