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Generalized functions associated with self-adjoint operators

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

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

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