Advisor(s)
Rudi Weikard
Committee Member(s)
Richard Brown
Yulia Karpeshina
Ryoichi Kawai
Claudio Morales
Document Type
Dissertation
Date of Award
2010
Abstract
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.
ProQuest Publication Number
ISBN
978-1-124-42737-9
Recommended Citation
Al Ahmad, Rami, "On Inverse Problem for Left-definite Discrete Sturm-Liouville Equations" (2010). All ETDs from UAB. 981.
https://digitalcommons.library.uab.edu/etd-collection/981
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