Integrability on the Abstract Wiener Space of Double Sequences and Fernique Theorem
- Authors
- Kim, J.-G.
- Issue Date
- 12-Oct-2021
- Publisher
- Hindawi Limited
- Citation
- Journal of Function Spaces, v.2021
- Journal Title
- Journal of Function Spaces
- Volume
- 2021
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/18156
- DOI
- 10.1155/2021/1667865
- ISSN
- 2314-8896
- Abstract
- 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. © 2021 Jeong-Gyoo Kim.
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Collections - School of Games > Game Software Major > 1. Journal Articles
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