Direct and Inverse Finite-Dimensional Spectral Problems on Graphs - Manfred Möller, Vyacheslav Pivovarchik

Direct and Inverse Finite-Dimensional Spectral Problems on Graphs

Buch | Softcover
XVI, 349 Seiten
2021 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-60486-8 (ISBN)
139,09 inkl. MwSt

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. 

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.

Erscheinungsdatum
Reihe/Serie Operator Theory: Advances and Applications
Zusatzinfo XVI, 349 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 563 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Schlagworte branching continued fraction • eigenvalues • eigenvectors and associated vectors • Hermite-Biehler polynomials • Lagrange polynomials • matrix operator pencil • Nevanlinna rational function • rational Stieltjes functions • rational Stieltjes functions • Stieltjes string • Sturm theorem • vibrations
ISBN-10 3-030-60486-1 / 3030604861
ISBN-13 978-3-030-60486-8 / 9783030604868
Zustand Neuware
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