# Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

## One radius theorem for the eigenfunctions of the invariant LaplacianHTML articles powered by AMS MathViewer

by E. G. Kwon
Proc. Amer. Math. Soc. 116 (1992), 27-34 Request permission

## Abstract:

Let $B$ be the open unit ball in ${{\mathbf {C}}^n}$ with its boundary $S$. Suppose that $\alpha \geq \tfrac {1}{2}$ and $u(z) = {(1 - {\left | z \right |^2})^{n(1 - \alpha )}}F(z)$ for some $F(z) \in C(\overline B )$. If for every $z \in B$ there corresponds an $r(z):0 < r(z) < 1$ and an automorphism ${\psi _z}$ with ${\psi _z}(0) = z$ such that $u(z) = \frac {1}{{{g_\alpha }(r(z))}}\int _S {u \circ {\psi _z}(r(z)\zeta )d\sigma (\zeta )} ,$ then $\tilde \Delta u(z) = - 4{n^2}\alpha (1 - \alpha )u(z),z \in B$. Here $\tilde \Delta$ is the invariant Laplacian and ${g_\alpha }(r)$ is the hypergeometric function $F(n - n\alpha ,n - n\alpha ,n;{r^2})$.
Similar Articles
• Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35P05, 35J05
• Retrieve articles in all journals with MSC: 35P05, 35J05