Taiwanese Journal of Mathematics

HALF INVERSE PROBLEMS FOR QUADRATIC PENCILS OF STURM-LIOUVILLE OPERATORS

Chuan-Fu Yang and Anton Zettl

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Abstract

Generally, the coefficients $p(x)$ and $q(x)$ of quadratic pencils of Sturm-Liouville operators are uniquely determined by two spectra or one spectrum and norming constants. In the present paper we show if $% p(x)$ and $q(x)$ are known on half of the domain interval, then one spectrum suffices to determine them uniquely on the other half.

Article information

Source
Taiwanese J. Math., Volume 16, Number 5 (2012), 1829-1846.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406800

Digital Object Identifier
doi:10.11650/twjm/1500406800

Mathematical Reviews number (MathSciNet)
MR2970688

Zentralblatt MATH identifier
1256.34013

Subjects
Primary: 34A55: Inverse problems 34B24: Sturm-Liouville theory [See also 34Lxx]
Secondary: 35K57: Reaction-diffusion equations 45C05: Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75]

Keywords
Sturm-Liouville operators inverse theorems quadratic pencils

Citation

Yang, Chuan-Fu; Zettl, Anton. HALF INVERSE PROBLEMS FOR QUADRATIC PENCILS OF STURM-LIOUVILLE OPERATORS. Taiwanese J. Math. 16 (2012), no. 5, 1829--1846. doi:10.11650/twjm/1500406800. https://projecteuclid.org/euclid.twjm/1500406800


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