Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-23T18:58:43.129Z Has data issue: false hasContentIssue false
  • English
  • Français

Mean value properties of generalised eigenfunctions†

Published online by Cambridge University Press:  20 January 2009

Eberhard Gerlach
Eberhard Gerlach
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver 168, B.C.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Some Hilbert spaces of continuous functions satisfying a mean value property are studied in which the generalised eigenfunctions of any selfadjoint operator again satisfy the same mean value property. Applications are made to nullspaces of some differential operators. The classes of functions involved in these applications are less general than those studied by K. Maurin (6); however, the Hilbert space norms may be arbitrary, while Maurin only considered L2-norms.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 2 , December 1970 , pp. 155 - 158
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

REFERENCES

(1) Friedman, A. and Littman, W., Functions satisfying the mean value property, Trans. Amer. Math. Soc. 102 (1962), 167–180.Google Scholar
(2) Gerlach, E., On spectral representation for selfadjoint operators. Expansion in generalized eigenelements, Ann. Inst. Fourier (Grenoble) 15 (1965), fasc. 2, 537–574.CrossRefGoogle Scholar
(3) Gerlach, E., On the analyticity of generalized eigenfunctions (case of real variables), Ann. Inst. Fourier (Grenoble) 18 (1968), fasc. 2, 11–16.CrossRefGoogle Scholar
(4) Kac, G. I., Generalized eigenfunctions on a locally compact group and de- compositions of unitary representations, Trudy Moskov. Mat. Obšč. 10 (1961), 3–40 (Russian).Google Scholar
(5) Leland, K. O., A characterization of analyticity IT, Proc. Amer. Math. Soc. 19 (1968), 519–527.CrossRefGoogle Scholar
(6) Maurin, K., Analyticity of generalized eigenfunctions, Bull. Acad. Polon. Sci. Sir. sci. math. astr. phys. 14 (1966), 685–687.Google Scholar
(7) Maurin, K., Allgemeine Eigenfunktionsentwicklungen, unitare Darstellungen lokal kompakter Gruppen und automorphe Funktionen, Math. Ann. 165 (1966), 204–222.CrossRefGoogle Scholar
(8) Mdchlin, S. G., The problem of the minimum of a quadratic functional (Holden-Day, San Francisco, 1965).Google Scholar
(9) Pietsch, A., Nukleare Funktionenraume, Math. Nachr. 33 (1967), 377–384.CrossRefGoogle Scholar
(10) Pietsch, A., Absolut p-summierende Abbildungen in normierten Raumen, Studia Math. 28 (1967), 333–353.CrossRefGoogle Scholar
(11) Wloka, J., Nukleare Raume aus M.K.-Funktionen, Math. Z. 92 (1966), 295–306.CrossRefGoogle Scholar