scholarly journals Inverse Scattering Problem for Sturm-Liouville Operator with Discontinuity Conditions on the Positive Half Line

2021 ◽  
Author(s):  
Özge AKÇAY
Keyword(s):  
Inverse Scattering ◽  
Liouville Operator ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Half Line ◽  
Sturm Liouville ◽  
Discontinuity Conditions ◽  
Positive Half

scholarly journals Inverse scattering problem for Sturm-Liouville operator on one-vertex noncompact graph with a cycle

2011 ◽  
Vol 42 (3) ◽  
pp. 365-384 ◽  
Author(s):  
Mikhail Ignatiev
Keyword(s):  
Inverse Problem ◽  
Differential Operator ◽  
Uniqueness Theorem ◽  
Inverse Scattering ◽  
Liouville Operator ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Order Differential Operator ◽  
Sturm Liouville ◽  
Noncompact Graph

A scattering problem is studied for second-order differential operator on one-vertex noncompact graph with a cycle and with standard matching conditions in the vertex. A uniqueness theorem for a corresponding inverse problem is proved and a procedure for solving the problem is provided.

scholarly journals Inverse spectral-scattering problem for the Sturm-Liouville operator on a noncompact star-type graph

2013 ◽  
Vol 44 (3) ◽  
pp. 327-349 ◽  
Author(s):  
Sergey Buterin ◽  
G. Freiling
Keyword(s):  
Finite Number ◽  
Spectral Data ◽  
Liouville Operator ◽  
Scattering Problem ◽  
Internal Vertex ◽  
Scattering Data ◽  
Half Line ◽  
Matching Conditions ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville

We study the Sturm-Liouville operator on a noncompact star-type graph consisting of a finite number of compact and noncompact edges under standard matching conditions in the internal vertex. We introduce and investigate the so-called spectral-scat\-tering data, which generalize the classical spectral data for the Sturm-Liouville operator on the half-line and the scattering data on the line. Developing the idea of the method of spectral mappings we prove that the specification of the spectral-scattering data uniquely determines the Sturm-Liouville operator on the graph.

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