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Generalized functions associated with self-adjoint operators

Part of: Distributions, generalized functions, distribution spaces Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

Liu Shangping
Liu Shangping
Affiliation:
Institute of MathematicsChinese Academy of Sciences Beijing 100080China e-mail: [email protected]
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Abstract

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In this paper, from several commutative self-adjoint operators on a Hilbert space, we define a class of spaces of fundamental functions and generalized functions, which are characterized completely by selfadjoint operators. Specially, using the common eigenvectors of these self-adjoint operators, we give the general form of expansion in series of generalized functions

Keywords

generalized functionself-adjoint operatorcompletenessnuclearity

MSC classification

Secondary: 46F05: Topological linear spaces of test functions, distributions and ultradistributions 47B25: Symmetric and selfadjoint operators (unbounded)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 3 , June 2000 , pp. 301 - 311
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Chin-Cheng, Chou, Séries de Fourier et théorie des distributions (Éditions Scientifiques, Beijing, 1983).Google Scholar
[2]Gel'fand, I. M. and Vilenkin, N. Ya., Generalized Functions. IV. Applications of harmonic analysis (Academic Press, New York, 1964).Google Scholar
[3]Halmos, P. R., A Hilber space problem book, Graduate Texts in Math. 19 (Springer, New York, 1982).CrossRefGoogle Scholar
[4]Reed, M. and Simon, B., Methods of modern physics. I. Functional analysis (Academic Press, New York, 1980).Google Scholar
[5]Riesz, F. and Sz.-Nagy, B., Leçons d'analyse fonctionnelle, 4th edition (Akad. Kiadó, Budapest, 1965).Google Scholar
[6]Schwartz, L., Théorie des distributions (Hermann, Paris, 1966).Google Scholar