On Spectral Theory of Elliptic Operators

the long version

This book contains results obtained by the authors in 1980-1992 and partially published in mathematical journals; some of them have not been translated into English before. The results relate to estimates of the first eigenvalue and the negative spectrum of the Schrödinger operator, as well as to estimates of eigenvalues and eigenfunctions. The first part of the book is of introductory character and contains the required tools from the theory of functional spaces, spectral theory, and the theory of elliptic boundary-value problems. It is essentially self-contained and can be used as a textbook by students.