Abelian theorems for distributional Kontorovich–Lebedev and Mehler–Fock transforms of general order

Benito J. González; Emilio R. Negrín

doi:10.1215/17358787-2019-0002

Abstract

Our goal in this article is to derive Abelian theorems for the Kontorovich–Lebedev and Mehler–Fock transforms of general order over distributions of compact support and over certain spaces of generalized functions.

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Benito J. González. Emilio R. Negrín. "Abelian theorems for distributional Kontorovich–Lebedev and Mehler–Fock transforms of general order." Banach J. Math. Anal. 13 (3) 524 - 537, July 2019. https://doi.org/10.1215/17358787-2019-0002

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Received: 28 September 2018; Accepted: 8 January 2019; Published: July 2019

First available in Project Euclid: 13 March 2019

zbMATH: 07083759

MathSciNet: MR3978935

Digital Object Identifier: 10.1215/17358787-2019-0002

Subjects:

Primary: 46F12

Secondary: 47G10

Keywords: distributions of compact support , general order , generalized functions , Kontorovich–Lebedev transform , Legendre function , Mehler–Fock transform , modified Bessel (or Macdonald) function

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