Direct and Inverse Sturm-Liouville Problems

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Sprache: Englisch

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Beschreibung

This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems.
The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.

Zusammenfassung

Explains in detail direct and simple methods for solving direct and inverse Sturm-Liouville and scattering problems on finite and infinite intervals

Includes a brief introduction to the notion and properties of transmutation operators

Formulates some of the most typical direct and inverse spectral and scattering problems

Inhaltsverzeichnis

Introduction.- Preliminaries on Sturm-Liouville equations.- Finite interval.- Half-line.- Quantum scattering problem on the half-line.- Scattering problem on the line.- Inverse scattering transform method.- Main transmutation operators.- Series representations.- Series representations for the Jost solution.- Sturm-Liouville problems on finite intervals.- Spectral problems on infinite intervals.- The inverse problem on a finite interval.- Solving the inverse problem on a half-line.- Inverse quantum scattering on the half-line.- Inverse scattering on the line.

Details

Erscheinungsjahr:	2020
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Frontiers in Mathematics
Inhalt:	xi 154 S. 1 s/w Illustr. 27 farbige Illustr. 154 p. 28 illus. 27 illus. in color.
ISBN-13:	9783030478483
ISBN-10:	3030478483
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Kravchenko, Vladislav V.
Auflage:	1st ed. 2020
Hersteller:	Springer International Publishing Springer International Publishing AG Frontiers in Mathematics
Maße:	240 x 168 x 10 mm
Von/Mit:	Vladislav V. Kravchenko
Erscheinungsdatum:	29.07.2020
Gewicht:	0,294 kg