Functions and Analysis

    

Reproducing Kernels, Theta Functions and Fundamental Inequalities

Authors: Saburou Saitoh

At first, I will introduce simply the analytical and classical reproducing kernels on the complex plane. Here, firstly, we recall the representations of reproducing kernels in terms of the theta functions that were obtained by D. A. Hejhal, J. D. Fay and A. Yamada. Indeed, the materials stated here are in Yamada's papers.Then, we will consider their meanings from the viewpoints of reproducing kernel theory, in particular, from the viewpoint of inequalities. We will find many important open problems. (The Second Lecture at Peking University on 3 October, 2026)

Comments: 15 Pages.

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[v1] 2026-10-03 20:30:01

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