E-Book Overview
"This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic Schro'9adinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators.
E-Book Content
Spectral Analysis of Differential Operators Interplay Between Spectral and Oscillatory Properties
World Scientific Monograph Series in Mathematics Eds:
Ron Donagi (University of Pennsylvania), Rafael de la Llave (University of Texas) and Mikhail Shubin (Northeastern University)
Published VOl. 1:
Almgren's Big Regularity Paper : Q-Valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-Minimizing Rectifiable Currents up to Codimension 2 Eds. V. Scheffer and J. E. Taylor
VOl. 2:
Dynamics and Mission Design Near Libration Points Vol. I Fundamentals: The Case of Collinear Libration Points by G. Gomez, J. Llibre, R. Martinez and C. Simo
VOl. 3:
Dynamics and Mission Design Near Libration Points Vol. II Fundamentals: The Case of Triangular Libration Points by G. Gomez, J. Llibre, R. Martinez and