An Inverse Sturm-Liouville Problem with Mixed Given Data

In general the potential function q(x) in a Sturm-Liouville problem is uniquely determined by two spectra. It is shown here that if q(x) is prescribed over the interval (1/2, 1), then a single spectrum suffices to determine q(x) on the interval $(0, \frac {1}{2})$.

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1978-06, Vol.34 (4), p.676-680
Main Authors: Hochstadt, Harry, Lieberman, Burton
Format: Article
Language:English
Subjects:
Boundary conditions
Eigenvalues
Entire functions
Inverse problems
Mathematical functions
Mathematical intervals
Mathematical theorems
Sine function
Spectral theory
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Summary:In general the potential function q(x) in a Sturm-Liouville problem is uniquely determined by two spectra. It is shown here that if q(x) is prescribed over the interval (1/2, 1), then a single spectrum suffices to determine q(x) on the interval $(0, \frac {1}{2})$.
ISSN:0036-1399
1095-712X
DOI:10.1137/0134054