# 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monatshefte f�r Mathematik Springer Journals

# Generalized functions and Laguerre expansions

, Volume 184 (1) – Apr 6, 2017
25 pages

/lp/springer_journal/generalized-functions-and-laguerre-expansions-dOlfDquXYj
Publisher
Springer Vienna
Subject
Mathematics; Mathematics, general
ISSN
0026-9255
eISSN
1436-5081
D.O.I.
10.1007/s00605-017-1045-y
Publisher site
See Article on Publisher Site

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