Executive Summary : | The study aims to investigate three problems related to Toeplitz operators, the uncertainty principle for Fourier-Wigner transforms, and Bochner-Riesz means. The first problem concerns Toeplitz operators on Fock space, where the product of two Toeplitz operators with bounded symbols is zero. The second problem is regrading the uncertainty principle for Fourier-Wigner transforms, where the finite linear combination of Fourier-Wigner transforms satisfy a decay condition. The third problem is on Bochner-Riesz means, which is a classical question about whether the Bochner-Riesz mean of an L^p function on the Euclidean space converges to the function in the L^p norm. Although there are several known results, the problem is not completely solved. The study aims to address similar questions in the context of Symmetric spaces. |