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INVERSE SPECTRAL PROBLEMS FOR STURM–LIOUVILLE OPERATORS WITH SINGULAR POTENTIALS. IV. POTENTIALS IN THE SOBOLEV SPACE SCALE

Published online by Cambridge University Press:  30 May 2006

Rostyslav O. Hryniv  and
Yaroslav V. Mykytyuk
Rostyslav O. Hryniv
Affiliation:
Institute for Applied Problems of Mechanics and Mathematics, 3B Naukova St., 79601 Lviv, Ukraine ([email protected]) Lviv National University, 1 Universytetska St., 79602 Lviv, Ukraine ([email protected])
Yaroslav V. Mykytyuk
Affiliation:
Institute for Applied Problems of Mechanics and Mathematics, 3B Naukova St., 79601 Lviv, Ukraine ([email protected]) Lviv National University, 1 Universytetska St., 79602 Lviv, Ukraine ([email protected])
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Abstract

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We solve the inverse spectral problems for the class of Sturm–Liouville operators with singular real-valued potentials from the Sobolev space $W^{s-1}_2(0,1)$, $s\in[0,1]$. The potential is recovered from two spectra or from one spectrum and the norming constants. Necessary and sufficient conditions for the spectral data to correspond to a potential in $W^{s-1}_2(0,1)$ are established.

Keywords

Primary 34A55Secondary 34B2434L0534L20inverse spectral problemsSturm–Liouville operatorssingular potentialsSobolev spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 2 , June 2006 , pp. 309 - 329
Copyright
Copyright © Edinburgh Mathematical Society 2006