Abstract:
We show the estimation of the logarithmic Sobolev constant and give the gradient estimates of heat semigroups. We study
Wiener’s lemma for localized integral operators on a Hilbert space We consider the stability of localized operators including infinite matrices. We derived an explicit gradient estimates and show the first Neumann eigenvalue on the manifolds with boundary. Also a second fundamental form and gradient of Neumann semigroups are considered .The positvity and negativity with compactness of the ground state energy for the Schrödinger operator on a Hilbert space are shown. We investigate the intrinsic ultracontractivity for
Schrödinger operators based on fractional Laplacian and semigroups on a Hilbert space.