Authors:
- 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
Part of the book series: Frontiers in Mathematics (FM)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (16 chapters)
-
Front Matter
-
Typical Problem Statements
-
Front Matter
-
-
Transmutation Operators and Series Representations for Solutions of Sturm-Liouville Equations
-
Front Matter
-
-
Solution of Direct Sturm-Liouville Problems
-
Front Matter
-
-
Solution of Inverse Sturm-Liouville Problems
-
Front Matter
-
About this book
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.
Authors and Affiliations
-
Department of Mathematics, Cinvestav, Querétaro, Mexico
Vladislav V. Kravchenko
Bibliographic Information
Book Title: Direct and Inverse Sturm-Liouville Problems
Book Subtitle: A Method of Solution
Authors: Vladislav V. Kravchenko
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/978-3-030-47849-0
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-47848-3Published: 29 July 2020
eBook ISBN: 978-3-030-47849-0Published: 28 July 2020
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: XI, 154
Number of Illustrations: 1 b/w illustrations, 27 illustrations in colour
Topics: Analysis, Operator Theory