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Inverse Problems
| Speaker: |
Marco Veneroni
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| Date: |
Wednesday April 4, 2007 |
| Title: |
Inverse eigenvalue
problems
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Abstract
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We study the Sturm-Liouville
eigenvalue problem in canonical form. First we focus on the direct
problem, i.e. determining eigenvalues and eigenfunctions for a given
parameter function and we recall some classical results of existence,
uniqueness and characterization. Then we consider the inverse spectral
problem (i.e. determining the parameter function for a given sequence
of eigenvalues), paying particular attention to the subject of
uniqueness. As an example, we give an application of the previous
results to a parabolic initial boundary problem. Finally, we discuss
some related numerical reconstruction techniques.
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