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Eigenfunction expansion of generalized functions

Published online by Cambridge University Press:  22 January 2016

J. N. Pandey  and
R. S. Pathak
J. N. Pandey
Affiliation:
Centre de Recherches Mathematiques, Université de Montréal and Department of Mathematics, Carleton University
R. S. Pathak
Affiliation:
Centre de Recherches Mathematiques, Université de Montréal and Department of Mathematics, Carleton University
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Expansions of generalized functions have been investigated by many authors. Korevaar [11], Widlund [20], Giertz [8], Walter [19] developed procedures for expanding generalized functions of Korevaar [12], Temple [17], and Lighthill [13], Expansions of certain Schwartz distributions [15] into series of orthonormal functions were given by Zemanian [23] (see also Zemanian [24]) and thereby he extended a number of integral transforms to distributions. The method involved in his work is very much related to the Hilbert space technique and is of somewhat different character from those used in most of the works on integral transforms such as [24, chapters 1-8]. Other works that discuss orthogonal series expansions involving generalized functions are by Bouix [1, chapter 7], Braga and Schönberg [2], Gelfand and Shilov [7, vol. 3, chapter 4] and Warmbrod [21].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 72 , December 1978 , pp. 1 - 25
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

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