Bibliography
Garsia, A. M.,A Note on the Mean Value Property, Trans. Amer. Math. Soc.102, 181–186 (1962).
Friedman, A. andLittman, W.,Functions Satisfying the Mean Value Property, Trans. Amer. Math. Soc.102, 167–180 (1962).
Aczél, J., Haruki, H., McKierman, M. A., andSakovič, G. N.,General and Regular Solutions of Functional Equations Characterizing Harmonic Polynomials, Aequationes Math.1, 37–53, (1968).
Swiatak, H.,The Regularity of the Distributional Solutions⋯, Aequationes Math.1, 6–19 (1968).
Kakutani, S. andNagumo, M., About the Functional Equation\(\sum\limits_{v = 0}^{n - 1} {f\left( {z + e^{\frac{{2v\pi i}}{n}} \xi } \right) = nf\left( z \right)} \), (Jap.) Zenk. Sugaku Danwa.,66, 10–12 (1935).
Choquet, G. andDeny, J.,Sur quelques propriétés de moyenne caractéristiques des fonctions harmoniques, Bull. Soc. Math. France,72, 118–140 (1944).
Ciesielski, Z.,Some Properties of Convex Functions of Higher Order, Ann. Polon. Math.7, 1–7 (1959).
Kemperman, J. H. B.,A General Functional Equation, Trans. Amer. Math. Soc.86, 28–56 (1957).
McKiernan, M. A.,On Vanishing n-th Ordered Differences and Hamel Bases, Ann. Polon. Math.19, 331–336 (1967).
Djoković, D. Ž.,A Representation Theorem for (x 1 − 1) (x 2 − 1)⋯(x n − 1)and Its Applications, submitted to Ann. Polon. Math.
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McKiernan, M.A. Boundedness on a set of positive measure and the mean value property characterizes polynomials on a spaceV n . Aeq. Math. 4, 31–36 (1970). https://doi.org/10.1007/BF01817742
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DOI: https://doi.org/10.1007/BF01817742