Characterizations of Fock-type spaces of eigenfunctions on R<sup>n</sup>
In this paper, we prove a norm equivalence for an exponential type weighted integral of an eigenfunction and its derivative on R<sup>n</sup>. As applications, we characterize Fock-type spaces of eigenfunctions on R<sup>n</sup> in terms of Lipschitz type conditions and double...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022852?viewType=HTML |
| _version_ | 1818113408656998400 |
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| author | Xi Fu Xiaoqiang Xie |
| author_facet | Xi Fu Xiaoqiang Xie |
| author_sort | Xi Fu |
| collection | DOAJ |
| description | In this paper, we prove a norm equivalence for an exponential type weighted integral of an eigenfunction and its derivative on R<sup>n</sup>. As applications, we characterize Fock-type spaces of eigenfunctions on R<sup>n</sup> in terms of Lipschitz type conditions and double integral conditions. These obtained results are extensions of the corresponding ones in classcial Fock space. |
| first_indexed | 2024-12-11T03:34:22Z |
| format | Article |
| id | doaj.art-09a6ded301b448be9f1addf678b5bb35 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-11T03:34:22Z |
| publishDate | 2022-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-09a6ded301b448be9f1addf678b5bb352022-12-22T01:22:17ZengAIMS PressAIMS Mathematics2473-69882022-06-0178155501556210.3934/math.2022852Characterizations of Fock-type spaces of eigenfunctions on R<sup>n</sup>Xi Fu 0Xiaoqiang Xie1Department of Mathematics, College of Arts and Sciences, Shanghai Polytechnic University, Shanghai 201209, ChinaDepartment of Mathematics, College of Arts and Sciences, Shanghai Polytechnic University, Shanghai 201209, ChinaIn this paper, we prove a norm equivalence for an exponential type weighted integral of an eigenfunction and its derivative on R<sup>n</sup>. As applications, we characterize Fock-type spaces of eigenfunctions on R<sup>n</sup> in terms of Lipschitz type conditions and double integral conditions. These obtained results are extensions of the corresponding ones in classcial Fock space.https://www.aimspress.com/article/doi/10.3934/math.2022852?viewType=HTMLeigenfunctionfock spacelipschitz conditiondouble integral condition |
| spellingShingle | Xi Fu Xiaoqiang Xie Characterizations of Fock-type spaces of eigenfunctions on R<sup>n</sup> AIMS Mathematics eigenfunction fock space lipschitz condition double integral condition |
| title | Characterizations of Fock-type spaces of eigenfunctions on R<sup>n</sup> |
| title_full | Characterizations of Fock-type spaces of eigenfunctions on R<sup>n</sup> |
| title_fullStr | Characterizations of Fock-type spaces of eigenfunctions on R<sup>n</sup> |
| title_full_unstemmed | Characterizations of Fock-type spaces of eigenfunctions on R<sup>n</sup> |
| title_short | Characterizations of Fock-type spaces of eigenfunctions on R<sup>n</sup> |
| title_sort | characterizations of fock type spaces of eigenfunctions on r sup n sup |
| topic | eigenfunction fock space lipschitz condition double integral condition |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022852?viewType=HTML |
| work_keys_str_mv | AT xifu characterizationsoffocktypespacesofeigenfunctionsonrsupnsup AT xiaoqiangxie characterizationsoffocktypespacesofeigenfunctionsonrsupnsup |