On the Fock Kernel for the Generalized Fock Space and Generalized Hypergeometric Series
In this paper, we compute the reproducing kernel Bm,αz,w for the generalized Fock space Fm,α2ℂ. The usual Fock space is the case when m=2. We express the reproducing kernel in terms of a suitable hypergeometric series 1Fq. In particular, we show that there is a close connection between B4,αz,w and...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/1365674 |
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| author | Jong-Do Park |
| author_facet | Jong-Do Park |
| author_sort | Jong-Do Park |
| collection | DOAJ |
| description | In this paper, we compute the reproducing kernel Bm,αz,w for the generalized Fock space Fm,α2ℂ. The usual Fock space is the case when m=2. We express the reproducing kernel in terms of a suitable hypergeometric series 1Fq. In particular, we show that there is a close connection between B4,αz,w and the error function. We also obtain the closed forms of Bm,αz,w when m=1,2/3,1/2. Finally, we also prove that Bm,αz,z~eαzmzm−2 as ∣z∣⟶∞. |
| format | Article |
| id | doaj-art-03b85d23c5ad43d6a95db08bed385463 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-03b85d23c5ad43d6a95db08bed3854632025-02-03T07:24:03ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/13656741365674On the Fock Kernel for the Generalized Fock Space and Generalized Hypergeometric SeriesJong-Do Park0Department of Mathematics, Kyung Hee University, Seoul 02447, Republic of KoreaIn this paper, we compute the reproducing kernel Bm,αz,w for the generalized Fock space Fm,α2ℂ. The usual Fock space is the case when m=2. We express the reproducing kernel in terms of a suitable hypergeometric series 1Fq. In particular, we show that there is a close connection between B4,αz,w and the error function. We also obtain the closed forms of Bm,αz,w when m=1,2/3,1/2. Finally, we also prove that Bm,αz,z~eαzmzm−2 as ∣z∣⟶∞.http://dx.doi.org/10.1155/2021/1365674 |
| spellingShingle | Jong-Do Park On the Fock Kernel for the Generalized Fock Space and Generalized Hypergeometric Series Journal of Function Spaces |
| title | On the Fock Kernel for the Generalized Fock Space and Generalized Hypergeometric Series |
| title_full | On the Fock Kernel for the Generalized Fock Space and Generalized Hypergeometric Series |
| title_fullStr | On the Fock Kernel for the Generalized Fock Space and Generalized Hypergeometric Series |
| title_full_unstemmed | On the Fock Kernel for the Generalized Fock Space and Generalized Hypergeometric Series |
| title_short | On the Fock Kernel for the Generalized Fock Space and Generalized Hypergeometric Series |
| title_sort | on the fock kernel for the generalized fock space and generalized hypergeometric series |
| url | http://dx.doi.org/10.1155/2021/1365674 |
| work_keys_str_mv | AT jongdopark onthefockkernelforthegeneralizedfockspaceandgeneralizedhypergeometricseries |