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523: １３２人目の素数さん [] 2023/03/18(土) 18:06:47.16 ID:M09HE8oG

>>513
>Saitoh's conjecture
>Guanが解いた

ありがとう、キーワード
"Saitoh's" conjecture math sharp effective strong openness conjecture
で検索すると、下記だね。最後に、下記があるね
”Zhou for bringing me to Saitoh’s conjecture when I was a postdoctor”
”Professor Saburou Saitoh for helpful discussions and encouragements”

（参考）
https://arxiv.org/pdf/2205.08044.pdf
MODULES AT BOUNDARY POINTS, FIBERWISE BERGMAN
KERNELS, AND LOG-SUBHARMONICITY II? ON STEIN
MANIFOLDS
SHIJIE BAO AND QI’AN GUAN
Abstract. In this article, we consider Bergman kernels related to modules
at boundary points on Stein manifolds and obtain a log-subharmonicity property of the Bergman kernels. As applications, we obtain a lower estimate of
weighted L2
integrals on Stein manifolds and reprove an effectiveness result of
the strong openness property of modules at boundary points on Stein manifolds.
[27] Q.A. Guan, A proof of Saitoh’s conjecture for conjugate Hardy H2 kernels. J. Math. Soc.Japan 71 (2019), no. 4, 1173?sC1179.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1677671318/523

524: １３２人目の素数さん [] 2023/03/18(土) 18:07:24.36 ID:M09HE8oG

>>523
つづき
　↓
https://arxiv.org/abs/1712.04207
[Submitted on 12 Dec 2017 (v1), last revised 11 Mar 2018 (this version, v2)]
A proof of Saitoh's conjecture for conjugate Hardy H2 kernels
Qi'an Guan
In this article, we obtain a strict inequality between the conjugate Hardy H2 kernels and the Bergman kernels on planar regular regions with n>1 boundary components, which is a conjecture of Saitoh.
https://arxiv.org/pdf/1712.04207.pdf
P1
When t = w, R?(z, w￣) denotes R?w(z, w￣) for simplicity. When z = w, R?(z) denotes
R?(z, z￣) for simplicity.
Let B(z, w￣) be the Bergman kernel on D. When z = w, B(z) denotes B(z, z￣)
for simplicity.
In [11] (see also [8] and [12]), the following so-called Saitoh’s conjecture was
posed (backgrounds and related results could be referred to Hejhal’s paper [7] and
Fay’s book [4]).
Conjecture 1.1. (Saitoh’s Conjecture) If n > 1, then R?(z) > πB(z).
In the present article, we give a proof of the above Conjecture.
Theorem 1.1. Conjecture 1.1 holds.
One of the ingredients of the present article is using the concavity of minimal L^2
integrations in [5].

Acknowledgements. The author would like to thank Professor Xiangyu , and Professor Fusheng
Deng, Professor Takeo Ohsawa, Professor Saburou Saitoh for helpful discussions
and encouragements. The author would also like to thank the hospitality of Beijing
International Center for Mathematical Research.
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1677671318/524

530: １３２人目の素数さん [] 2023/03/18(土) 19:05:42.47 ID:M09HE8oG

>>523
Saitoh's conjecture
について、調べた結果

https://arxiv.org/pdf/1712.04207.pdf
A proof of Saitoh's conjecture for conjugate Hardy H2 kernels
Qi'an Guan
[8] S. Saitoh, Theory of reproducing kernels and its applications. Pitman Research Notes in
Mathematics Series, 189. Longman Scientific & Technical, Harlow; copublished in the United
States with John Wiley & Sons, Inc., New York, 1988. x+157 pp. ISBN: 0-582-03564-3

(下記サイトから冒頭2ページのみダウンロード可能)
https://link.springer.com/chapter/10.1007/978-1-4757-2987-0_15
Home  Reproducing Kernels and their Applications  Chapter
Applications of the General Theory of Reproducing Kernels
Saburou Saitoh

https://www.jstage.jst.go.jp/article/emath1996/2003/Spring-Meeting/2003_Spring-Meeting_66/_pdf/-char/ja
数学会/総合講演・企画特別講演アブストラクト/2003 巻 (2003) Spring-Meeting 号
再生核の理論について 斎藤三郎(群馬大工)

0はじめに
再生核の理論は,1921年と1922年に出版された論文にそれぞれゼゲー核とベルグマン核と呼ばれ
る典型的な再生核が初めて現れ,その後それらの再生核は多くの人々によって研究され,複素解析学
における大きな理論に発展してきました.他方,再生核の一般的な理論は1950年にアロンシャイン
によって出版された論文同で一応完成されていました.さらに一般理論について,超関数の理論の
創始者ローランシュワルツが1964年に140ページを越える大論文【401を出版していることは大変
注目されます.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1677671318/530

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