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References
Akcoglu, M.A., Sharpe, R.W.: Ergodic theory and boundaries. Trans. Am. Math. Soc.132, 447–460 (1968)
Baxter, J.R.: Restricted mean values and harmonic functions. Trans. Am. Math. Soc.167, 451–463 (1972)
Baxter, J.R.: Harmonic functions and mass cancellation. Trans. Am. Math. Soc.245, 375–384 (1978)
Bliedtner, J., Hansen, W.: Potential theory-An analytic and probabilistic approach to balayage (Universitext) Berlin Heidelberg New York: Springer 1986
Boukricha, A., Hansen, W., Hueber, H.: Continuous solutions of the generalized Schrödinger equation and perturbation of harmonic spaces. Expos. Math.5, 97–135, (1987)
Brunel, A.: Propriété restreinte de valuer moyenne caractérisant les fonctions harmoniques bornées sur un ouvert dans ℝ2 (selon D. Heath et L. Orey). Séminaire Goulaouic-Schwartz, exposé No. XIV. Paris (1971–1972)
Burckel, R.B.: A strong converse to Gauss's mean value theorem. Am. Math. Mon.87, 819–820 (1980)
Doob, J.L.: Classical potential theory and its probabilistic counterpart. (Grundlehren Math. Wiss. vol. 262) Berlin Heidelberg New York: Springer 1984
Feller, W.: Boundaries induced by nonnegative matrices. Trans. Am. Math. Soc.83, 19–54 (1956)
Fenton, P.C.: Functions having the restricted mean value property. J. Lond. Math. Soc.14, 451–458 (1976)
Fenton, P.C.: On sufficient conditions for harmonicity. Trans. Am. Math. Soc.253, 139–147 (1979)
Fenton, P.C.: On the restricted mean value property. Proc. Am. Math. Soc.100, 477–481 (1987)
Gong, X.: Functions with the restricted mean value property. J. Xiamen Univ., Nat. Sci.27, 611–615 (1988)
de Guzmán, M.: Differentiation of integrals in ℝ2 (Lect. Notes Math., vol. 481) Berlin Heidelberg New York: Springer 1975
Hansen, W.: Valeurs propres pour l'opérateur de Schrödinger. In: Bouleau, N. et al (eds.) Séminaire de théorie du potentiel. Paris. No. 9 (Lect. Notes Math., vol. 1393 pp. 117–134) Berlin Heidelberg New York: Springer 1989
Hansen, W., Ma, Zh.: Perturbation by differences of, unbounded potentials. Math. Ann.287, 553–569 (1990)
Hansen, W., Nadirashvili, N.: A converse to the mean value theorem for harmonic functions. To appear in Acta Math.
Heath, D.: Functions possessing restricted mean value properties. Proc. Am. Math. Soc.41, 588–595 (1973)
Helms, L.L.: Introduction to potential theory. New York: Wiley 1969
Huckemann, F.: On the ‘one circle’ problem for harmonic functions. J. Lond. Math. Soc.29, 491–497 (1954)
Kellogg, O.D.: Converses of Gauss's theorem on the arithmetic mean. Trans. Am. Math. Soc.36, 227–242 (1934)
Littlewood, J.L.: Some problems in real and complex analysis. Massachusetts. Hath. Math. Monographs 1968
Netuka, I.: Harmonic functions and mean value theorems (Czech). Čas. Pěstování Mat.100, 391–409 (1975)
Veech, W.A.: A zero-one law for a class of random walks and a converse to Gauss' mean value theorem. Ann. Math.97, 189–216 (1973)
Veech, W.A.: A converse to the mean value theorem for harmonic functions. Am. J. Math.97, 1007–1027 (1975)
Veselý, J.: Restricted mean value property in axiomatic potential theory. Commentat. Math. Univ. Carol.23, 613–628 (1982)
Volterra, V.: Alcune osservazioni sopra proprietà atte individuare una funzione. Atti Reale Accad. Lincei18, 263–266 (1909)