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

DOI10.1215/17358787-2019-0002zbMath1425.46027OpenAlexW2921369046WikidataQ128225375 ScholiaQ128225375MaRDI QIDQ2314360

Benito J. González, Emilio R. Negrin

Publication date: 22 July 2019

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bjma/1552464163

zbMATH Keywords

Kontorovich-Lebedev transformMehler-Fock transformmodified Bessel functionabelian theoremdistribution of compact support

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Integral operators (47G10)

Related Items

Lebedev–Skalskaya transforms and allied operators on certain function spaces ⋮ Abelian theorems for Laplace and Mehler-Fock transforms of generalized functions ⋮ Abelian theorems for Laplace, Mellin and Stieltjes transforms over distributions of compact support and generalized functions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ An operational calculus for a Mehler-Fock type index transform on distributions of compact support

Cites Work

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• \(L^{p}\)-inequalities and Parseval-type relations for the Mehler-Fock transform of general order
• A convolution connected with the Kontorovich-Lebedev transform
• On the Convolution Theorem of the Mehler-Fock-Transform for a Class of Generalized Functions (I)
• On the Convolution Theorem of the Mehler-Fock-Transform for a Class of Generalized Functions (II)
• The Kontorovich–Lebedev transformation on distributions of compact support and its inversion
• NewL^p-boundedness properties for the Kontorovich–Lebedev and Mehler–Fock transforms
• Some Abelian Theorems for the Distributional Hankel and K Transformations

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