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Direct and inverse Sturm-Liouville p...

Kravchenko, Vladislav V.

Direct and inverse Sturm-Liouville problemsa method of solution /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Direct and inverse Sturm-Liouville problemsby Vladislav V. Kravchenko.
其他題名:	a method of solution /
作者:	Kravchenko, Vladislav V.
出版者:	Cham :Springer International Publishing :2020.
面頁冊數:	xi, 154 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Inverse problems (Differential equations)
電子資源:	https://doi.org/10.1007/978-3-030-47849-0
ISBN:	9783030478490$q(electronic bk.)

Direct and inverse Sturm-Liouville problemsa method of solution /
Kravchenko, Vladislav V.

Direct and inverse Sturm-Liouville problemsa method of solution /[electronic resource] :by Vladislav V. Kravchenko. - Cham :Springer International Publishing :2020. - xi, 154 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8046. - Frontiers in mathematics..

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.

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.

ISBN: 9783030478490$q(electronic bk.)

Standard No.: 10.1007/978-3-030-47849-0doiSubjects--Topical Terms:

189581
Inverse problems (Differential equations)

LC Class. No.: QA378.5 / .K73 2020

Dewey Class. No.: 515.357

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505 0 $a 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.
520 $a 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.
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