Integrability on the Abstract Wiener Space of Double Sequences and Fernique Theorem
The integrability of a function defined on the abstract Wiener space of double Fourier coefficients is explored. The abstract Wiener space is also a Hilbert space. We define an orthonormal system of the Hilbert space to establish a measure and integration on the abstract Wiener space. We examine the...
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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/10.1155/2021/1667865 |
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| _version_ | 1832546064394092544 |
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| author | Jeong-Gyoo Kim |
| author_facet | Jeong-Gyoo Kim |
| author_sort | Jeong-Gyoo Kim |
| collection | DOAJ |
| description | The integrability of a function defined on the abstract Wiener space of double Fourier coefficients is explored. The abstract Wiener space is also a Hilbert space. We define an orthonormal system of the Hilbert space to establish a measure and integration on the abstract Wiener space. We examine the integrability of a function eα·2 defined on the abstract Wiener space for Fernique theorem. With respect to the abstract Wiener measure, the integral of the function turns out to be convergent for α<1/2. The result provides a wider choice of the constant α than that of Fernique. |
| format | Article |
| id | doaj-art-65a7a86a84d44bc798210ca76307ad09 |
| 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-65a7a86a84d44bc798210ca76307ad092025-02-03T07:24:03ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/16678651667865Integrability on the Abstract Wiener Space of Double Sequences and Fernique TheoremJeong-Gyoo Kim0Hongik University, Sejong, Republic of KoreaThe integrability of a function defined on the abstract Wiener space of double Fourier coefficients is explored. The abstract Wiener space is also a Hilbert space. We define an orthonormal system of the Hilbert space to establish a measure and integration on the abstract Wiener space. We examine the integrability of a function eα·2 defined on the abstract Wiener space for Fernique theorem. With respect to the abstract Wiener measure, the integral of the function turns out to be convergent for α<1/2. The result provides a wider choice of the constant α than that of Fernique.http://dx.doi.org/10.1155/2021/1667865 |
| spellingShingle | Jeong-Gyoo Kim Integrability on the Abstract Wiener Space of Double Sequences and Fernique Theorem Journal of Function Spaces |
| title | Integrability on the Abstract Wiener Space of Double Sequences and Fernique Theorem |
| title_full | Integrability on the Abstract Wiener Space of Double Sequences and Fernique Theorem |
| title_fullStr | Integrability on the Abstract Wiener Space of Double Sequences and Fernique Theorem |
| title_full_unstemmed | Integrability on the Abstract Wiener Space of Double Sequences and Fernique Theorem |
| title_short | Integrability on the Abstract Wiener Space of Double Sequences and Fernique Theorem |
| title_sort | integrability on the abstract wiener space of double sequences and fernique theorem |
| url | http://dx.doi.org/10.1155/2021/1667865 |
| work_keys_str_mv | AT jeonggyookim integrabilityontheabstractwienerspaceofdoublesequencesandferniquetheorem |