Inverse Spectral Problems for Sturm-Liouville Operators with Singular Potentials, II. Reconstruction by Two Spectra**The work was partially supported by Ukrainian Foundation for Basic Research DFFD under grant No. 01.07/00172. R. H. acknowledges support of the Alexander von Humboldt Foundation.

2004 ◽  
pp. 97-114 ◽  
Author(s):  
Rostyslav O. Hryniv ◽  
Yaroslav V. Mykytyuk
Keyword(s):  
Basic Research ◽  
Inverse Spectral Problems ◽  
Singular Potentials ◽  
Spectral Problems ◽  
Alexander Von Humboldt ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Liouville Operators

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

2006 ◽  
Vol 49 (2) ◽  
pp. 309-329 ◽  
Author(s):  
Rostyslav O. Hryniv ◽  
Yaroslav V. Mykytyuk
Keyword(s):  
Sobolev Space ◽  
Spectral Data ◽  
Sufficient Conditions ◽  
Inverse Spectral Problems ◽  
Singular Potentials ◽  
Spectral Problems ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Necessary And Sufficient ◽  
Liouville Operators

AbstractWe 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.

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