Advisory Committee Chair
Advisory Committee Members
Date of Award
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
ON INVERSE PROBLEMS FOR LEFT-DEFINITE DISCRETE STURM-LIOUVILLE EQUATIONS RAMI ALAHMAD APPLIED MATHEMATICS ABSTRACT We are interested in studying a class of discrete Sturm-Liouville problems called left-de nite problems corresponding to a positive definite quadratic form associated with the left side of the Sturm-Liouville equations. Important tools for studying Sturm-Liouville equations are the eigenfunction expansions and the corresponding Fourier transforms. Here, we introduce the generalized Fourier transform associated with the left-definite problems. Also, we extend the discussion to inverse problems for discrete Sturm-Liouville equations. In inverse spectral problems, the task is to find a coefficient in the equation using the spectral data. We discuss the uniqueness of spectral inverse problems for the discrete left-definite Sturm-Liouville Problems. We introduce the Jost solution corresponding to the left-definite Sturm-Liouville equation to find the coefficients of the left-definite Sturm-Liouville operator by applying the principles of inverse scattering problems. Finally, we find the coefficients of the left-definite Sturm-Liouville operator using the zeros of the Jost solution by applying the principles of inverse resonance problems.
Alahmad, Rami, "On Inverse Problem for Left-definite Discrete Sturm-Liouville Equations" (2010). All ETDs from UAB. 981.