Almansi theorem and mean value formula for quaternionic slice-regular functions

DOI10.1007/s00006-020-01078-4zbMath1461.30118OpenAlexW3080725807MaRDI QIDQ2204140

Alessandro Perotti

Publication date: 15 October 2020

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-020-01078-4

zbMATH Keywords

mean value propertyPoisson formulaquaternionic polynomialszonal harmonicsslice-regular functionsAlmansi theorem

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Spherical harmonics (33C55) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items (6)

Cauchy-Riemann operators and local slice analysis over real alternative algebras ⋮ Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation ⋮ A quaternionic Bernstein theorem ⋮ A local Cauchy integral formula for slice-regular functions ⋮ Eigenvalue problems for slice functions ⋮ Slice-by-slice and global smoothness of slice regular and polyanalytic functions

Cites Work

• Slice regular functions on real alternative algebras
• Slice monogenic functions
• A new theory of regular functions of a quaternionic variable
• Almansi decomposition for Dunkl operators
• Harmonic Function Theory
• Regular Functions of a Quaternionic Variable
• The algebra of slice functions
• (Discrete) Almansi type decompositions: an umbral calculus framework based on osp(1|2) symmetries
• Division algebras of slice functions
• Almansi‐type theorems in Clifford analysis
• Topics in Clifford Analysis
• Distributions, partial differential equations, and harmonic analysis

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