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ASYMPTOTICS OF A TAU-FUNCTION AND TOEPLITZ DETERMINANTS WITH SINGULAR GENERATING FUNCTIONS

Department of Mathematics, California Polytechnic State University, San Luis Obispo, CA 93407, USA

and

Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606, Japan

Fellow of the Japan Society for the Promotion of Science.

Permanent address: Department of Mathematics and Institute of Theoretical Dynamics, University of California, Davis, CA 95616, USA.

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https://doi.org/10.1142/S0217751X92003732Cited by:13 (Source: Crossref)

Abstract

We compute the short distance asymptotics of a tau-fucntion appearing in the work of Sato, Miwa, and Jimbo on holonomic quantum fields, We show that these asymptotics are determined by the Widom operator. This same operator is fundamental in the asymptotics of Toeplitz determinants with singular generating fucntions.