Inverse spectral problems for Sturm–Liouville differential operators on a finite interval

2009 ◽  
Vol 17 (7) ◽  
Author(s):  
V. A. Yurko
Keyword(s):  
Differential Operators ◽  
Finite Interval ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Sturm Liouville ◽  
Inverse Spectral

Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials

2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Liubov Efremova ◽  
Gerhard Freiling
Keyword(s):  
Numerical Solution ◽  
Differential Operators ◽  
Finite Interval ◽  
Inverse Spectral Problems ◽  
Numerical Examples ◽  
Spectral Problems ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Liouville Operators

AbstractWe consider Sturm-Liouville differential operators on a finite interval with discontinuous potentials having one jump. As the main result we obtain a procedure of recovering the location of the discontinuity and the height of the jump. Using our result, we apply a generalized Rundell-Sacks algorithm of Rafler and Böckmann for a more effective reconstruction of the potential and present some numerical examples.

scholarly journals Inverse spectral problems for differential operators on a graph with a rooted cycle

2009 ◽  
Vol 40 (3) ◽  
pp. 271-286 ◽  
Author(s):  
V. Yurko
Keyword(s):  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Inverse Spectral Problems ◽  
Matching Conditions ◽  
Spectral Problems ◽  
Sturm Liouville ◽  
Inverse Spectral

An inverse spectral problem is studied for Sturm-Liouville differential operators on graphs with a cycle and with standard matching conditions in internal vertices. A uniqueness theorem is proved, and a constructive procedure for the solution is provided.

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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