Representation formulas for the general derivatives of the fundamental solution to the Cauchy-Riemann operator in Clifford analysis and applications

DOI10.4171/ZAA/1096zbMath1018.30037OpenAlexW2042686367MaRDI QIDQ1848655

Denis Constales, Rolf Sören Krausshar

Publication date: 21 January 2003

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/1096

zbMATH Keywords

fundamental solutionDirichlet seriesCauchy-Riemann operatorpermutation productshypercomplex variable

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

Related Items (8)

Monogenic modular forms in two and several real and complex vector variables ⋮ On the relation between the growth and the Taylor coefficients of entire solutions to the higher-dimensional Cauchy--Riemann system in \(\mathbb R^{n+1}\) ⋮ Entire monogenic functions of given proximate order and continuous homomorphisms ⋮ The multiplication of the Clifford-analytic Eisenstein series. ⋮ Infinite-order differential operators acting on entire hyperholomorphic functions ⋮ Basics of a generalized Wiman-Valiron theory for monogenic Taylor series of finite convergence radius ⋮ Further results on the asymptotic growth of entire solutions of iterated Dirac equations in ℝn ⋮ On Cauchy estimates and growth orders of entire solutions of iterated Dirac and generalized Cauchy–Riemann equations

Cites Work

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• Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces
• On a new type of Eisenstein series in Clifford analysis
• On the singularities of functions with values in a Clifford algebra
• Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen
• Monogenic muitiperiodic functions in clifford analysis
• Power series representation for monogenic functions in based on a permutational product
• Some connections between clifford analysis and complex analysis

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