Direct and Inverse Sturm-Liouville Problems
A Method of Solution
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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.
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.
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
Autor*in
Vladislav V. Kravchenko
Themen in »Direct and Inverse Sturm-Liouville Problems«
scattering problem inverse scattering problem spectral parameter power series Neumann series of Bessel functions Jost solution transmutation operator transformation operator