Closed form of the generalized Green’s function for the Helmholtz operator on the two-dimensional unit sphere

DOI10.1063/1.2203430zbMath1112.35049OpenAlexW2086336148MaRDI QIDQ3441935

Radosław Szmytkowski

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.2203430

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Harmonic analysis on homogeneous spaces (43A85) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Elliptic equations on manifolds, general theory (58J05) Green's functions for ordinary differential equations (34B27) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (5)

Towards uniqueness of degenerate axially symmetric Killing horizon ⋮ Wavelet based solutions to the Poisson and the Helmholtz equations on the \(n\)-dimensional unit sphere ⋮ On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order) ⋮ Exact sum rules for heterogeneous spherical drums ⋮ The Stability of Localized Spot Patterns for the Brusselator on the Sphere

Uses Software

• SPHEREPACK

Cites Work

• On integral formulas of the (unit) sphere and their application to numerical computation of integrals
• On the diffraction of high-frequency waves by a cone of arbitrary shape
• The diffraction of a high-frequency acoustic wave by a narrow-angle absolutely rigid cone of arbitrary shape
• The High-Frequency Diffraction of Electromagnetic Waves by Cones of Arbitrary Cross Sections
• Boundary Value Problems of Mathematical Physics: Volume 2
• On Evaluation of the Diffraction Coefficients for Arbitrary "Nonsingular" Directions of a Smooth Convex Cone
• The Computation of Conical Diffraction Coefficients in High-Frequency Acoustic Wave Scattering
• Diffraction of scalar waves by an impedance cone of arbitrary cross-section.
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