Elliptic transmutation I

DOI10.1017/S0308210500017534zbMath0539.35003MaRDI QIDQ3326075

Robert W. Carroll

Publication date: 1982

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

zbMATH Keywords

transmutationsHilbert transformsLaplace-Beltrami operatorsaxially symmetric potential theory

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Scattering theory for PDEs (35P25) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Spherical harmonics (33C55) Higher-order elliptic equations (35J30) General integral transforms (44A05)

Related Items

Some remarks on the generalized Gelfand-Levitan equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a partial differential equation with two singular lines
• A fractional integral operator corresponding to negative powers of a certain second-order differential operator
• Some remarks on transmutation, scattering theory, and special functions
• Scattering techniques in transmutation and some connection formulas for special functions
• A new proof of a Paley-Wiener type theorem for the Jacobi transform
• Integral representations for Jacobi polynomials and some applications
• Paley-Wiener type theorems for a differential operator connected with symmetric spaces
• The convolution structure for Jacobi function expansions
• On the uniqueness of generalized axially symmetric potentials
• Opérateurs de Delsarte et problèmes mixtes
• Some Remarks on Transmutation
• Scattering techniques for a one dimensional inverse problem in geophysics
• Inverse scattering techniques in geophysics
• Some Remarks on singular pseudodifferential operators
• Research announcement
• On the Boundedness of Lowndes' Operators
• 19.—Improved Boundedness Conditions for Lowndes' Operators
• Related singular problems and the generalized Hilbert transform
• Transmutation and separation of variables
• A Modification of Hilbert Transforms, the Weyl Integral and Functional Equations
• On a Modification of the Hilbert Transform
• A generalisation of the Erdélyi-Kober operators
• Hilbert Transforms, Plemelj Relations, and Fourier Transforms of Distributions
• On the Ranges of Certain Fractional Integrals
• On axially symmetric flows
• On axially symmetric flow and the method of generalized electrostatics
• Generalized axially symmetric potential theory
• The singular solutions and the cauchy problem for generalized Tricomi equations
• On a class of differential equations in mechanics of continua