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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Mehler-Fock transforms of generalized functions via the method of adjoints


Authors: Benito J. González and Emilio R. Negrin
Journal: Proc. Amer. Math. Soc. 125 (1997), 3243-3253
MSC (1991): Primary 44A15, 46F12
DOI: https://doi.org/10.1090/S0002-9939-97-03957-9
MathSciNet review: 1403129
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Abstract: In this paper we analyse the Mehler-Fock transform of generalized functions via the method of adjoints. For a distribution of compact support, we prove that its Mehler-Fock transform agrees with its transform via the kernel method. A Paley-Wiener type theorem is established.


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Additional Information

Benito J. González
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 Canary Islands, Spain

Emilio R. Negrin
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 Canary Islands, Spain
Email: bjglez@ull.es, enegrin@ull.es

DOI: https://doi.org/10.1090/S0002-9939-97-03957-9
Keywords: Mehler-Fock transform, Legendre function, generalized functions, distributions of compact support, Paley-Wiener type theorem
Received by editor(s): January 2, 1996
Received by editor(s) in revised form: April 24, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society