Direct and Inverse Finite-Dimensional Spectral Problems on Graphs

1. Auflage 2020
ISBN: 978-3-030-60483-7
Verlag: Springer International Publishing

Buch, Englisch, Band 283, 349 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 717 g

Reihe: Operator Theory: Advances and Applications

Considering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings. The direct problem of finding the eigenvalues as well as the inverse problem of finding strings with a prescribed spectrum are considered. This monograph gives a comprehensive and self-contained account on the subject, thereby also generalizing known results. The interplay between the representation of rational functions and their zeros and poles is at the center of the methods used. The book also unravels connections between finite dimensional and infinite dimensional spectral problems on graphs, and between self-adjoint and non-self-adjoint finite-dimensional problems.

This book is addressed to researchers in spectral theory of differential and difference equations as well as physicists and engineers who may apply the presented results and methods to their research. 

Zielgruppe

Research

Autoren/Hrsg.

Pivovarchik, Vyacheslav

Möller, Manfred

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

Stieltjes strings.- Vibrations of star graphs.- Damped vibrations.- Trees.- Miscellaneous results.- Discrete Laplacians.- Relation between finite and infinite dimensional problems on graphs.- Rational Nevanlinna and Stieltjes Functions.