Inequalities for Schroedinger operators and laws of the iterated logarithm

Dahae You, Purdue University

Abstract

In the first part of this thesis we derive inequalities for multiple integrals from which inequalities for ratios of integrals of heat kernels of certain Schrödinger operators follows. Such ratio inequalities imply inequalities for the partition functions of these operators which extend the spectral gap results. In the second part, we study the law of the iterated logarithm originated from Kolmogorov's law of the iterated logarithm for random variables. In 1988, R. Bañuelos, I. Klemes and C. N. Moore proved law of the iterated logarithm for harmonic functions for the upper bound and in 1990, they proved the lower bound. In chapter 3, we derive laws of the iterated logarithm for L-harmonic functions where L is an elliptic operator.

Degree

Ph.D.

Advisors

Banuelos, Purdue University.

Subject Area

Mathematics

COinS