Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T16:44:47.307Z Has data issue: false hasContentIssue false
  • English
  • Français

ON A FRIEDRICHS EXTENSION RELATED TO UNBOUNDED SUBNORMALS-II

Published online by Cambridge University Press:  01 January 2008

SAMEER CHAVAN
SAMEER CHAVAN*
Affiliation:
Indian Institute of Science Education & Research (IISER) Pune-411008, India E-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

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.

We study the Friedrichs extensions of unbounded cyclic subnormals. The main result of the present paper is the identification of the Friedrichs extensions of certain cyclic subnormals with their closures. This generalizes as well as complements the main result obtained in [5]. Such characterizations lead to abstract Galerkin approximations, generalized wave equations, and bounded -functional calculi.

Keywords

Primary 41A6547B20Secondary 35K9041A1047A0747B32
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 1 , January 2008 , pp. 97 - 109
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Aronszajn, N., Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337–404.Google Scholar
2.Athavale, A. and Chavan, S., Sectorial forms and unbounded subnormals, Math. Proc. Cambridge Phil. Soc., to appear.Google Scholar
3.Conway, J., The theory of subnormal operators, Mathematical Surveys and Monographs, Vol. 36 (Amer. Math. Soc., Providence, 1991).Google Scholar
4.Chavan, S., Sectorial forms and unbounded subnormals, Ph.D Dissertation, University of Pune, 2006.Google Scholar
5.Chavan, S. and Athavale, A., On a Friedrichs extension related to unbounded subnormals, Glasgow Math. J. 48 (2006), 19–28.CrossRefGoogle Scholar
6.Edmonds, D. E. and Evans, W. D., Spectral Theory and Differential Operators, Oxford Science Publications, Clarendon Press, Oxford, 1987.Google Scholar
7.Markus, Hasse, The functional calculus for sectorial operators, Operator Theory Advances and Applications Vol.169 (Birkhd. a user, 2006).Google Scholar
8.Kato, T., Perturbation, Theory for Linear Operators, Springer-Verlag, New York, 1984.Google Scholar
9.Miklavčič, M., Applied functional analysis and partial differential equations (World Scientific, Singapore, 1998).CrossRefGoogle Scholar
10.Stochel, J. and Szafraniec, F., On normal extensions of unbounded operators. I, J. Operator Theory 14 (1985), 31–55.Google Scholar
11.Stochel, J. and Szafraniec, F., On normal extensions of unbounded operators II, Acta Sci. Math. (Szeged) 53 (1989), 153–177.Google Scholar
12.Stochel, J. and Szafraniec, F., On normal extensions of unbounded operators III, Spectral properties, Publ. RIMS, Kyoto Univ. 25 (1989), 105–139.Google Scholar