References
[A] A. Atzmon,Uniform approximation by linear combinations of translations and dilations of a function, J. London Math. Soc. (2)27 (1983), 51–54.
[B.S.T.] L. Brown, B. M. Schreiber and B. A. Taylor,Spectral synthesis and the Pompeiu problem, Ann. Inst. Fourier (Grenoble)23 (1973), 125–154.
[HR] E. Hewitt and K. A. Ross,Abstract Harmonic Analysis, Vol. II. Grundlehren 152, Springer-Verlag, Berlin-Göttingen-Heidelberg-New York, 1963 and 1970.
[N] D. J. Newman,Translates are always dense on the half line, Proc. Am. Math. Soc.21 (1969), 511–512.
[P] R. R. Phelps,Lectures on Choquet's Theorem, D. Van Nostrand, 1966.
[Wa] J. L. Walsh,A mean value theorem for polynomials and harmonic polynomials, Bull. Am. Math. Soc.42 (1936), 923–930.
[We] Y. Weit,A characterization of polynomials by convolution equations, J. London Math. Soc. (2)23 (1981), 455–459.
[Z1] L. Zalcman,Analyticity and the Pompeiu problem, Arch. Ratl. Mech. Anal.47 (1972), 237–254.
[Z2] L. Zalcman,Mean values and differential equations, Isr. J. Math.14 (1973), 339–352.
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Benyamini, Y., Weit, Y. Functions satisfying the mean value property in the limit. J. Anal. Math. 52, 167–198 (1981). https://doi.org/10.1007/BF02820477
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DOI: https://doi.org/10.1007/BF02820477