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Restriction theorem for the Fourier-Hermite transform associated with the normalized Hermite polynomials and the Ornstein-Uhlenbeck-Schrödinger equation (2207.06844v2)

Published 14 Jul 2022 in math.CA and math.FA

Abstract: 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.

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