Symplectic Difference Systems: Oscillation and Spectral Theory

Description

This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which are based on the recently developed central object - the comparative index. The book contains numerous results and citations, which were till now scattered only in journal papers. The book also provides new applications of the theory of matrices in this field, in particular of the Moore-Penrose pseudoinverse matrices, orthogonal projectors, and symplectic matrix factorizations. Thus it brings this topic to the attention of researchers and students in pure as well as applied mathematics. Front Matter ....Pages i-xv Motivation and Preliminaries (Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher)....Pages 1-81 Basic Theory of Symplectic Systems (Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher)....Pages 83-148 Comparative Index Theory (Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher)....Pages 149-200 Oscillation Theory of Symplectic Systems (Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher)....Pages 201-260 Discrete Symplectic Eigenvalue Problems (Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher)....Pages 261-396 Miscellaneous Topics on Symplectic Systems (Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher)....Pages 397-572 Back Matter ....Pages 573-593