Restriction theorem for the Fourier-Hermite transform associated with the normalized Hermite polynomials and the Ornstein-Uhlenbeck-Schrödinger equation

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 op...

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Bibliographic Details
Published in:arXiv.org 2022-07
Main Authors: Ghosh, Sunit, Swain, Jitendriya
Format: Article
Language:English
Subjects:
Hermite polynomials
Mathematical analysis
Orthonormal functions
Schrodinger equation
Theorems
Online Access:Get full text
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Summary: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 \(L=-\frac{1}{2}\Delta+\langle x, \nabla\rangle\) 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.
ISSN:2331-8422