Negative Spectra of Elliptic Operators

Abstract

We are going to discuss here estimates of the number of points in the negative spectrum of an elliptic operator. Such estimates are important for physical applications, especially in quantum mechanics. They are of interest for spectral theory; from the point of view of the theory of partial differential equations they provide an opportunity to define subspaces of finite codimension on which some embedding theorems are valid. This can be useful, for instance, in stating and studying boundary value problems. In particular, these estimates allow us to find stable subspaces of solutions to the corresponding parabolic equations.