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 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.

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 An inverse spectral problem for differential operators with integral delay

2011 ◽  
Vol 42 (3) ◽  
pp. 295-303 ◽  
Author(s):  
Yulia Kuryshova
Keyword(s):  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Liouville Operator ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Integral Transform ◽  
Main Tool ◽  
One Dimensional ◽  
Sturm Liouville ◽  
The Uniqueness Theorem

The uniqueness theorem is proved for the solution of the inverse spec- tral problem for second-order integro-di®erential operators on a ¯nite interval. These operators are perturbations of the Sturm-Liouville operator with convolution and one- dimensional operators. The main tool is an integral transform connected with solutions of integro-di®erential operators.

scholarly journals Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem

2004 ◽  
Vol 2004 (5) ◽  
pp. 435-451
Author(s):  
E. K. Ifantis ◽  
K. N. Vlachou
Keyword(s):  
Differential Equation ◽  
Probability Measure ◽  
Exact Solutions ◽  
Spectral Problem ◽  
Toda Lattice ◽  
Inverse Spectral Problem ◽  
Initial Conditions ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Inverse Spectral

Several inverse spectral problems are solved by a method which is based on exact solutions of the semi-infinite Toda lattice. In fact, starting with a well-known and appropriate probability measureμ, the solutionαn(t),bn(t)of the Toda lattice is exactly determined and by takingt=0, the solutionαn(0),bn(0)of the inverse spectral problem is obtained. The solutions of the Toda lattice which are found in this way are finite for everyt>0and can also be obtained from the solutions of a simple differential equation. Many other exact solutions obtained from this differential equation show that there exist initial conditionsαn(0)>0andbn(0)∈ℝsuch that the semi-infinite Toda lattice is not integrable in the sense that the functionsαn(t)andbn(t)are not finite for everyt>0.

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