Hypersingular Integrals of Marchaud Type and the Inversion Problem for Potentials

DOI10.1002/MANA.19941650116zbMath0832.31004OpenAlexW2160606203MaRDI QIDQ4846798

Boris Rubin

Publication date: 5 March 1996

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19941650116

zbMATH Keywords

fractional integralsoscillatory potentialsspherical potentialsparabolic potentialsinversion problem for Riesz potentialsregularized solutions to Abel type integral equations

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Numerical methods for ill-posed problems for integral equations (65R30) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Theoretical approximation of solutions to integral equations (45L05) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items (3)

Calderón's reproducing formula and singular integral operators on a real line ⋮ Inversion of potential-type operators with symbols degenerate on hyperboloids and paraboloids ⋮ Complex powers of degenerate differential operators connected with the Klein-Gordon-Fock operator

Cites Work

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• On certain singular integrals
• One-dimensional representation, inversion, and certain properties of the Riesz potentials of radial functions
• Inversion of parabolic potentials with \(L_ p\)-densities
• Inversion of potentials in \(R^ n\) by means of Gauss-Weierstrass integrals
• Abel integral equations. Analysis and applications
• Fractional integrals and weakly singular integral equations of the first kind in the \(n\)-dimensional ball
• Table errata: Table of integrals, series and products [English translation of the fourth Russian edition, Academic Press, New York, 1965; MR 33 #5952 by I. S. Gradšteĭn and I. M. Ryžik]

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