Function theories for the Yukawa and Helmholtz equations

DOI10.1216/RMJM/1181072194zbMath0844.30032OpenAlexW1997299918MaRDI QIDQ1912623

J. W. Dettman, Louis R. Bragg

Publication date: 5 September 1996

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181072194

zbMATH Keywords

heat equationDirichlet problemsHelmholtz equationstransmutationsNeumann problemsYukawa equations

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Series solutions to PDEs (35C10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Partial differential equations of mathematical physics and other areas of application (35Q99) Generalized function theory (30G99)

Related Items (2)

A quasi inner product approach for constructing solution representations of Cauchy problems ⋮ Panharmonic functions: mean value properties and related topics

Cites Work

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• Analogous function theories for the heat, wave, and Laplace equations
• Analogous function theories for certain singular partial differential equations
• Some analogies from classical analysis in the theory of heat conduction
• On operator calculus for related partial differential equations
• Expansions of solutions of certain hyperbolic and elliptic problems in terms of Jacobis polynomials
• Yukawan potential theory
• An outline of the theory of pseudoanalytic functions
• Expansions in Terms of Heat Polynomials and Associated Functions
• A Class of Related Dirichlet and Initial Value Problems
• Hilbert Transforms in Yukawan Potential Theory

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