The Hankel transform of some classes of generalized functions and connections with fractional integration

DOI10.1017/S0308210500010477zbMath0398.44002OpenAlexW2315639400MaRDI QIDQ4183203

A. C. McBride

Publication date: 1978

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500010477

zbMATH Keywords

Bessel FunctionHankel TransformFunctional IntegrationGeneralized Integral TransformationsIntegral Transforms in Distribution SpacesMapping Properties

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Operations with distributions and generalized functions (46F10) Fractional derivatives and integrals (26A33) Integral transforms of special functions (44A20)

Related Items (3)

Integral transforms of generalized functions ⋮ A generalization of \(H_{\mu}\)-spaces and Hankel transforms ⋮ Solution of dual integral equations of Titchmarsh type using generalised functions

Cites Work

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• On the Hankel transform of distributions
• A Theory of Fractional Integration for Generalized Functions
• Some Classes of Watson Transforms and Related Integral Equations for Generalized Functions
• A note on the spaces F_P,µ
• A theory of fractional integration for generalised functions II
• A Technique for Studying the Boundedness and Extendability of Certain Types of Operators
• On Spaces of Type $H_\mu $ and Their Hankel Transformations
• On Schwartz’s Hankel Transformation of Certain Spaces of Distributions
• On the Ranges of Certain Fractional Integrals
• ON FRACTIONAL INTEGRALS AND DERIVATIVES
• SOME REMARKS ON HANKEL TRANSFORMS
• ON FRACTIONAL INTEGRATION AND ITS APPLICATION TO THE THEORY OF HANKEL TRANSFORMS
• COMPLEX FOURIER--BESSEL TRANSFORMS

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