Sharp Inequalities for Ratios of Partition Functions of Schrödinger Operators

This paper derives 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 proved by R. Bañuelos and P. Méndez-Hernández and B. Davis.