Explicit formulas for the Green's function and the Bergman kernel for monogenic functions in annular shaped domains in \(\mathbb{R}^{n+1}\)
type: Item
instance of: scholarly article
title: Explicit formulas for the Green's function and the Bergman kernel for monogenic functions in annular shaped domains in \(\mathbb{R}^{n+1}\)
zbMATH Open document ID: 1206.30068
author: Dennis Grob
author: D. Constales
author: R. S. Kraußhar
published in: Results in Mathematics
publication date: 2010-10-14T00:00:00Z
review text: Given the harmonic Green's function of a domain, its hypercomplex Bergman kernel for the corresponding class of functions of Clifford or quaternionic analysis can be obtained by applying from the left- and from the right-hand side the proper differential Cauchy-Riemann, or Dirac, operators. Thus the authors first obtain explicit representation formulas for the harmonic Green's function for orthogonal sectors of the annulus of the unit ball in \(\mathbb R^n\), and then construct the respective Bergman kernels. This applies in order to give an explicit analytic representation of the solutions to an \(n\)-dimensional Dirichlet problem in annular shaped domains arising in the context of heat conduction.
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 31B20
zbMATH DE Number: 5800221
zbMATH Keywords: Bergman kernel
zbMATH Keywords: Green's function
zbMATH Keywords: annular domains
zbMATH Keywords: Clifford anlysis
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: heat conduction
reviewed by: M. Shapiro
MaRDI profile type: Publication
full work available at URL: s00025-009-0015-7
OpenAlex ID: W2036165296
cites work: Szegő projections for Hardy spaces of monogenic functions and applications
cites work: Hypercomplex Function Theory and Hilbert Modules with Reproducing Kernel
cites work: Q3310867
cites work: Q4857168
cites work: The Bergman and Szegö kernels for separately monogenic functions
cites work: Bergman kernels for rectangular domains and multiperiodic functions in Clifford analysis
cites work: The Bergman Kernels for the half-ball and for fractional wedge-shaped domains in Clifford Analysis
cites work: On the Navier–Stokes equations with free convection in three‐dimensional unbounded triangular channels
cites work: Q4003806
cites work: Aspects of Dirac operators in analysis
cites work: Quaternionic analysis and elliptic boundary value problems
cites work: Q4857181
cites work: On the Bergmann kernel function in hyperholomorphic analysis
DOI: 10.1007/S00025-009-0015-7
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description: scientific article; zbMATH DE number 5800221