Some classical problems in harmonie analysis
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Date
2023
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Abstract
This thesis focuses on certain classical problems in harmonic analysis in connection with
mathematical physics. We begin with the Fourier analysis on the Euciidean space, discuss
some well known results, basic definitions, and review of recent developments that
motivates us to consider the problems discussed in the thesis.
We prove a restriction theorem for the Fourier-Hermite transform and obtain a Strichartz
estimate for systems of orthonormal fi.rnctions associated with the Hermite operator
H : -L, + lrl' on R.' for the range I I q < ffi as an application. Besides, we show an
optimal behavior of the constant in the Strichartz estimate as limit of a large number of
functions.
Description
Supervisor: Swain, Jitendriya
Keywords
StricharE Estimale, Restriction Theorem, Hermite Operator, Speeial Hermite Operator, Szeg\"0 Limit Theorem, Pseudo-differential Operator