Positive differentials, theta functions

and Hardy kernels

Author:
Akira Yamada

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1399-1408

MSC (1991):
Primary 30C40; Secondary 14K25

Published electronically:
January 29, 1999

MathSciNet review:
1476401

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a planar regular region whose Schottky double has genus and set . For fixed we determine the range of the function where is the Riemann theta function on . Also we introduce two weighted Hardy spaces to study the problem when the matrix is positive definite. The proof relies on new theta identities using Fay's trisecants formula.

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Additional Information

**Akira Yamada**

Affiliation:
Department of Mathematics and Informatics, Tokyo Gakugei University, Koganei, Tokyo 184, Japan

Email:
yamada@u-gakugei.ac.jp

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-04711-5

Keywords:
Positive differential,
theta function,
kernel function

Received by editor(s):
June 22, 1997

Received by editor(s) in revised form:
August 18, 1997

Published electronically:
January 29, 1999

Communicated by:
Albert Baernstein II

Article copyright:
© Copyright 1999
American Mathematical Society