Strichartz Estimates Associated with Certain Self-Adjoint Operators

Abstract

The main focus of this thesis is the study of Strichartz estimates and their extensions to systems of orthonormal functions associated with certain self-adjoint operators. In addition, we investigate a sharp Heisenberg-Pauli-Weyl uncertainty principle for the fractional Dunkl transform. We begin with the Fourier analysis on the Euclidean space, discuss some well known results, basic definitions, and and recent developments that motivate the problems discussed in the thesis.