On a Cauchy-type integral related to the Helmholtz operator in the plane

zbMath1069.30077MaRDI QIDQ1885510

Oleg F. Gerus, Michael V. Shapiro

Publication date: 5 November 2004

Published in: Boletín de la Sociedad Matemática Mexicana. Third Series (Search for Journal in Brave)

zbMATH Keywords

Helmholtz operatorquaternionCauchy-type integralhyperhomorphic function

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) CR structures, CR operators, and generalizations (32V05)

Related Items (13)

Boundary value problems for hyperholomorphic solutions of two dimensional Helmholtz equation in a fractal domain ⋮ Applications of the Clifford algebra valued boundary element method to electromagnetic scattering problems ⋮ Dirichlet-type problems for the two-dimensional Helmholtz operator in complex quaternionic analysis ⋮ On the 2D quaternionic metaharmonic layer potentials ⋮ Jump conditions for a metaharmonic double layer potential on rectifiable closed Jordan curves in R² ⋮ On the Cauchy theorem for hyperholomorphic functions of spatial variable ⋮ Higher order Dirichlet-type problems in 2D complex quaternionic analysis ⋮ On the Hilbert formulas and of change of integration order for some singular integrals in the unit circle ⋮ Poincaré-Bertrand formula on a piecewise Liapunov curve in two-dimensional ⋮ On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation ⋮ Dirichlet type problem for 2D quaternionic time-harmonic Maxwell system in fractal domains ⋮ On hyperholomorphic functions of the space variable ⋮ 2D quaternionic time-harmonic Maxwell system in elliptic coordinates

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