Symplectic Difference Systems: Oscillation and Spectral Theory

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.

List of contents

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.

Summary

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.

Product details

• Authors: Roman ¿imon Hilscher, Ond¿ej Do¿lý, Ondre Doslý, Ondrej Doslý, Ondřej Došlý, Juli Elyseeva, Julia Elyseeva, Roman Simon Hilscher, Roma Simon Hilscher, Roman Simon Hilscher, Roman Šimon Hilscher
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.01.2019
• EAN: 9783030193720
• ISBN: 978-3-0-3019372-0
• No. of pages: 593
• Dimensions: 162 mm x 239 mm x 41 mm
• Weight: 1069 g
• Illustrations: XV, 593 p. 7 illus. in color.
• Series: Pathways in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; B, Funktionalanalysis und Abwandlungen, Mathematics and Statistics, Difference equations, Functional equations, Difference and Functional Equations, Functional analysis & transforms, Operator Theory, recessive solution at infinity, focal point