On the theorem of S. Kakutani, M. Nagumo and J. L. Walsh for the mean value property of harmonic and complex polynomials

DOI10.2140/PJM.1981.94.113zbMath0472.39002OpenAlexW2061843585MaRDI QIDQ1157723

Shigeru Haruki

Publication date: 1981

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1981.94.113

zbMATH Keywords

harmonic polynomialsharmonic functionshomogeneous polynomialsmean-valuesdifference functional equationsKakutani-Nagumo-Walsh

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Difference operators (39A70) Polynomials and rational functions of one complex variable (30C10)

Related Items (6)

The existence of solvable operators in the ideal ⋮ On certain generalizations of the Levi-Civita and Wilson functional equations ⋮ Characterization of polynomials as solutions of certain functional equations ⋮ Using Aichinger's equation to characterize polynomial functions ⋮ A note on monomials ⋮ Polytopes and the mean value property

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