Some classical problems in harmonie analysis

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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.
Supervisor: Swain, Jitendriya
StricharE Estimale, Restriction Theorem, Hermite Operator, Speeial Hermite Operator, Szeg\"0 Limit Theorem, Pseudo-differential Operator