Inverse problems of spectral analysis for the Sturm-Liouville operator with regular boundary conditions: I

2007 ◽  
Vol 43 (10) ◽  
pp. 1364-1375 ◽  
Author(s):  
A. S. Makin
Keyword(s):  
Spectral Analysis ◽  
Inverse Problems ◽  
Boundary Conditions ◽  
Liouville Operator ◽  
Regular Boundary ◽  
Sturm Liouville ◽  
Regular Boundary Conditions

Partial inverse problems for the Sturm–Liouville operator on a star-shaped graph with mixed boundary conditions

2018 ◽  
Vol 26 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Liouville Operator ◽  
Mixed Boundary ◽  
Constructive Method ◽  
Asymptotic Formulas ◽  
Riesz Basis Property ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Shaped Graph

AbstractThe Sturm–Liouville operator on a star-shaped graph with different types of boundary conditions (Robin and Dirichlet) in different vertices is studied. Asymptotic formulas for the eigenvalues are derived and partial inverse problems are solved: we show that the potential on one edge can be uniquely determined by different parts of the spectrum if the potentials on the other edges are known. We provide a constructive method for the solution of the inverse problems, based on the Riesz basis property of some systems of vector functions.

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