Symplectic Difference Systems: Oscillation and Spectral Theory

ISBN-13: 9783030193720 / Angielski / Twarda / 2019 / 593 str.

Ondrej Dosly; Julia Elyseeva; Roman Simon Hilscher

Opis

This monograph is devoted to covering the main results in the oscillation and spectral theory of symplectic difference systems. 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 based on the recently developed comparative index theory.In the last twenty years, various results from the qualitative theory of symplectic and Hamiltonian difference systems were obtained. However, there is no book or a survey paper presenting in a unified way the results of the qualitative theory of symplectic difference systems. This book fills this gap by providing numerous results and citations, which are till now scattered only in journal papers.

Spis treści

Motivation and Preliminaries.- Basic Theory of Symplectic Systems.- Comparative Index Theory.- Oscillation Theory of Symplectic Systems.- Discrete Symplectic Eigenvalue Problems.- Miscellaneous Topics on Symplectic Systems.

Blurb

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.