Generalized functions and Laguerre expansions

Generalized functions and Laguerre expansions In this paper we study and characterize expansions of distributions in the Zemanian spaces, $${\mathcal {H}}_{\mu }$$ H μ and its dual $${\mathcal {H}}_{\mu }^{\prime }$$ H μ ′ ( $$\mu \ge -\frac{1}{2}$$ μ ≥ - 1 2 ) with respect to Laguerre functions. We obtain as applications of this result, the kernel Theorem and a structure Theorem for $${\mathcal {H}}_{\mu }^{\prime }$$ H μ ′ . We also introduce a new algebra of generalized functions in the sense of J. F. Colombeau such that it satisfies interesting properties involving the Hankel transformation and Hankel convolution. Monatshefte f�r Mathematik Springer Journals

Generalized functions and Laguerre expansions

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Springer Vienna
Copyright © 2017 by Springer-Verlag Wien
Mathematics; Mathematics, general
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