Some remarks on the stability of a property related to the mean value theorem for harmonic functions
HTML articles powered by AMS MathViewer
- by Burton Randol
- Proc. Amer. Math. Soc. 114 (1992), 175-179
- DOI: https://doi.org/10.1090/S0002-9939-1992-1079707-7
- PDF | Request permission
Abstract:
Suppose $u$ is harmonic and of mean zero over a compact domain $D$. We study the extent to which the zero-set of $u$ must penetrate into the interior of $D$.References
- Philip J. Davis, Double integrals expressed as single integrals or interpolatory functionals, J. Approximation Theory 5 (1972), 276–307. MR 377069, DOI 10.1016/0021-9045(72)90018-4
- Philip J. Davis, The Schwarz function and its applications, The Carus Mathematical Monographs, No. 17, Mathematical Association of America, Buffalo, N.Y., 1974. MR 0407252
- Bernard Epstein, On the mean-value property of harmonic functions, Proc. Amer. Math. Soc. 13 (1962), 830. MR 140700, DOI 10.1090/S0002-9939-1962-0140700-0
- G. Mittag-Leffler, Sur la représentation analytique d’une branche uniforme d’une fonction monogène, Acta Math. 29 (1905), no. 1, 101–181 (French). cinquième note. MR 1555012, DOI 10.1007/BF02403200
- Makoto Sakai, Quadrature domains, Lecture Notes in Mathematics, vol. 934, Springer-Verlag, Berlin-New York, 1982. MR 663007
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 175-179
- MSC: Primary 31A05; Secondary 30C15, 31B05
- DOI: https://doi.org/10.1090/S0002-9939-1992-1079707-7
- MathSciNet review: 1079707