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Criticality of Schrödinger forms and recurrence of Dirichlet forms
http://hdl.handle.net/10112/0002002190
http://hdl.handle.net/10112/000200219050f149e9-8d2a-48e5-b7ed-304ad2b17e62
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
KU-1100-20230210-01.pdf (306 KB)
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| Item type | 学術雑誌論文 / Journal Article(1) | |||||
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| 公開日 | 2024-12-19 | |||||
| タイトル | ||||||
| タイトル | Criticality of Schrödinger forms and recurrence of Dirichlet forms | |||||
| 言語 | en | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | journal article | |||||
| アクセス権 | ||||||
| アクセス権 | open access | |||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||
| 著者 |
竹田, 雅好
× 竹田, 雅好× 上村, 稔大 |
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| 概要 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | Introducing the notion of extended Schrödinger spaces, we define the criticality and subcriticality of Schrödinger forms in the same manner as the recurrence and transience of Dirichlet forms, and give a sufficient condition for the subcriticality of Schrödinger forms in terms the bottom of spectrum. We define a subclass of Hardy potentials and prove that Schrödinger forms with potentials in this subclass are always critical, which leads us to optimal Hardy type inequality. We show that this definition of criticality and subcriticality is equivalent to that there exists an excessive function with respect to Schrödinger semigroup and its generating Dirichlet form through h-transform is recurrent and transient respectively. As an application, we can show the recurrence and transience of a family of Dirichlet forms by showing the criticality and subcriticaly of Schrödinger forms and show the other way around through h-transform, We give a such example with fractional Schrödinger operators with Hardy potential. | |||||
| 言語 | en | |||||
| 内容記述 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | The first author was supported in part by Grant-in-Aid for Scientific Research (No.18H01121(B)), Japan Society for the Promotion of Science. The second author was supported in part by Grant-in-Aid for Scientific Research (No.19K03552(C)), Japan Society for the Promotion of Science. | |||||
| 言語 | en | |||||
| 書誌情報 |
en : Transactions of the American Mathematical Society 巻 376, 号 6, p. 4145-4171, 発行日 2023-02-10 |
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| ISSN | ||||||
| 収録物識別子タイプ | PISSN | |||||
| 収録物識別子 | 00029947 | |||||
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| 収録物識別子タイプ | EISSN | |||||
| 収録物識別子 | 10886850 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA00865686 | |||||
| DOI | ||||||
| 関連タイプ | isVersionOf | |||||
| 識別子タイプ | DOI | |||||
| 関連識別子 | https://doi.org/10.1090/tran/8865 | |||||
| 権利 | ||||||
| 言語 | en | |||||
| 権利情報 | © Copyright 2024 American Mathematical Society | |||||
| 著者版フラグ | ||||||
| 出版タイプ | AM | |||||
| 出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||
| 出版者 | ||||||
| 出版者 | American Mathematical Society | |||||
| 言語 | en | |||||
| キーワード | ||||||
| 言語 | ja | |||||
| 主題Scheme | Other | |||||
| 主題 | 関西大学 | |||||
| キーワード | ||||||
| 言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | Kansai University | |||||
