ON HARMONICITY IN A DISC AND n-HARMONICITY

Title & Authors
ON HARMONICITY IN A DISC AND n-HARMONICITY
Lee, Jae-Sung;

Abstract
Let $\small{{\tau}\;{\neq}\;\delta_0}$ be either a power bounded radial measure with compact support on the unit disc D with $\tau(D)\; Keywords mean value property;harmonicity;n-harmonicity;convolution;spectrum; Language English Cited by References 1. P. Ahern, M. Flores, and W. Rudin, An invariant volume-mean-value property, J. Funct. Anal. 111 (1993), no. 2, 380–397. 2. J. Arazy and M. Englis, Iterates and the boundary behavior of the Berezin transform, Ann. Inst. Fourier (Grenoble) 51 (2001), no. 4, 1101–1133. 3. Y. Benyamini and Y. Weit, Harmonic analysis of spherical functions on SU(1, 1), Ann. Inst. Fourier (Grenoble) 42 (1992), no. 3, 671–694. 4. M. Englis, Functions invariant under the Berezin transform, J. Funct. Anal. 121 (1994), no. 1, 233–254. 5. H. Furstenberg, A Poisson formula for semi-simple Lie groups, Ann. of Math. (2) 77 (1963), 335–386. 6. H. Furstenberg, Boundaries of Riemannian symmetric spaces, Symmetric spaces (Short Courses, Washington Univ., St. Louis, Mo., 1969–1970), pp. 359–377. Pure and Appl. Math., Vol. 8, Dekker, New York, 1972. 7. Y. Katznelson and L. Tzafriri, On power bounded operators, J. Funct. Anal. 68 (1986), no. 3, 313–328. 8. J. Lee, Weighted Berezin transform in the polydisc, J. Math. Anal. Appl. 338 (2008), no. 2, 1489–1493. 9. W. Rudin, Function Theory in the Unit Ball of$C^n\$, Springer-Verlag, New York Inc., 1980.