Restriction theorem for the Fourier-Hermite transform associated with the normalized Hermite polynomials and the Ornstein-Uhlenbeck-Schrödinger equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2022
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| _version_ | 1866916645914542080 |
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| author | Ghosh, Sunit Swain, Jitendriya |
| author_facet | Ghosh, Sunit Swain, Jitendriya |
| contents | In this article, we prove the analogue theorems of Stein-Tomas and Srtichartz on the discrete surface restrictions of Fourier-Hermite transforms associated with the normalized Hermite polynomials and obtain the Strichartz estimate for the system of orthonormal functions for the Ornstein-Uhlenbeck operator $L=-\frac{1}{2}Δ+\langle x, \nabla\rangle$ on $\mathbb{R}^n$. Further, we show an optimal behavior of the constant in the Strichartz estimate as limit of a large number of functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_06844 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Restriction theorem for the Fourier-Hermite transform associated with the normalized Hermite polynomials and the Ornstein-Uhlenbeck-Schrödinger equation Ghosh, Sunit Swain, Jitendriya Classical Analysis and ODEs Functional Analysis 35Q41, 47B10, Secondary 35P10, 35B65 In this article, we prove the analogue theorems of Stein-Tomas and Srtichartz on the discrete surface restrictions of Fourier-Hermite transforms associated with the normalized Hermite polynomials and obtain the Strichartz estimate for the system of orthonormal functions for the Ornstein-Uhlenbeck operator $L=-\frac{1}{2}Δ+\langle x, \nabla\rangle$ on $\mathbb{R}^n$. Further, we show an optimal behavior of the constant in the Strichartz estimate as limit of a large number of functions. |
| title | Restriction theorem for the Fourier-Hermite transform associated with the normalized Hermite polynomials and the Ornstein-Uhlenbeck-Schrödinger equation |
| topic | Classical Analysis and ODEs Functional Analysis 35Q41, 47B10, Secondary 35P10, 35B65 |
| url | https://arxiv.org/abs/2207.06844 |