This book presents recent results in the following areas: spectral analysis of one-dimensional Schrodinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators. Several developments treated appear for the first time in a book. It is addressed to a wide group of specialists working in operator theory or mathematical physics.

Differential and more general self-adjoint operators involving singular interactions arise naturally in a range of subjects such as classical and quantum physics, chemistry, and electronics. This book is a systematic mathematical study of these operators, with particular emphasis on spectral and scattering problems. The methods discussed are based on a new concept of symplectic structure of the "boundary form." Suitable for researchers in analysis or mathematical physics, this volume could also be used as a text for an advanced course on the applications of analysis.