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| viXra.org > Functions and Analysis > 2610 |
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[3] viXra:2610.0011 [pdf] submitted on 2026-10-03 20:30:01
Authors: Saburou Saitoh
Comments: 15 Pages.
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)
Category: Functions and Analysis
[2] viXra:2610.0009 [pdf] submitted on 2026-10-03 20:25:02
Authors: Richard J. Mathar
Comments: 10 Pages.
The Multiple Zeta Value zeta(2,1) is a double sum over two positive integer indices. If these indices are restricted by parity to cover either only even or only odd positive integers, the Multiple Zeta Value splits into four non-overlapping subseries. The manuscript evaluates these four series in terms of the Riemann Zeta function, pi and log 2.
Category: Functions and Analysis
[1] viXra:2610.0005 [pdf] submitted on 2026-10-01 20:59:54
Authors: Saburou Saitoh
Comments: 60 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
The theory of reproducing kernels is very fundamental, beautiful and has many applications in analysis and numerical analysis as in the Pythagorean theorem. In this first lecture, I would like to intoroduce some general viewpoint for reproducing kernels and some essences of reproducing kernels. However, the theory is already much more developing widely and deeply on this century. (The First Lecture at Peking University on 1 October, 2026)
Category: Functions and Analysis
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