Book Details


Direct and Inverse Sturm-Liouville Problems

Publication year: 2020

ISBN: 978-3-030-47849-0

Internet Resource: Please Login to download 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.

Subject: Mathematics and Statistics, Analysis, Operator Theory, scattering problem, inverse scattering problem, spectral parameter power series, Neumann series of Bessel functions, Jost solution, transmutation operator, transformation operator