scholarly journals Eigenvalue asymptotics for Sturm–Liouville operators with singular potentials

2006 ◽  
Vol 238 (1) ◽  
pp. 27-57 ◽  
Author(s):  
R.O. Hryniv ◽  
Y.V. Mykytyuk
Keyword(s):  
Singular Potentials ◽  
Eigenvalue Asymptotics ◽  
Sturm Liouville ◽  
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.

Sturm-liouville operators with singular potentials

1999 ◽  
Vol 66 (6) ◽  
pp. 741-753 ◽  
Author(s):  
A. M. Savchuk ◽  
A. A. Shkalikov
Keyword(s):  
Singular Potentials ◽  
Sturm Liouville ◽  
Liouville Operators

scholarly journals An inverse spectral problem for Sturm-Liouville operators with singular potentials on arbitrary compact graphs

2019 ◽  
Vol 50 (3) ◽  
pp. 293-305
Author(s):  
S. V. Vasiliev
Keyword(s):  
Inverse Problems ◽  
Spectral Problem ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Singular Potentials ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Weyl Functions ◽  
Liouville Operators

Sturm-Liouville differential operators with singular potentials on arbitrary com- pact graphs are studied. The uniqueness of recovering operators from Weyl functions is proved and a constructive procedure for the solution of this class of inverse problems is provided.

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