Chapter 2. inverse sturm-liouville problem on the half-line: determining the sturm-liouville operator from spectral function

1987 ◽  
pp. 24-63
Keyword(s):  
Spectral Function ◽  
Liouville Operator ◽  
Liouville Problem ◽  
Half Line ◽  
Sturm Liouville

scholarly journals Asymptotic Behaviour of Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem with Retarded Argument

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Erdoğan Şen ◽  
Jong Jin Seo ◽  
Serkan Araci
Keyword(s):  
Boundary Value Problem ◽  
Liouville Operator ◽  
Liouville Problem ◽  
Asymptotic Formulas ◽  
Retarded Argument ◽  
Eigenvalues And Eigenfunctions ◽  
Transmission Coefficients ◽  
Discontinuous Boundary ◽  
Sturm Liouville ◽  
Special Case

In the present paper, a discontinuous boundary-value problem with retarded argument at the two points of discontinuities is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. This is the first work containing two discontinuities points in the theory of differential equations with retarded argument. In that special case the transmission coefficients and retarded argument in the results obtained in this work coincide with corresponding results in the classical Sturm-Liouville operator.

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.

scholarly journals Fundamental Spectral Theory of Fractional Singular Sturm-Liouville Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Erdal Bas
Keyword(s):  
Spectral Theory ◽  
Liouville Operator ◽  
Spectral Properties ◽  
Liouville Problem ◽  
Eigenvalues And Eigenfunctions ◽  
Sturm Liouville

We give the theory of spectral properties for eigenvalues and eigenfunctions of Bessel type of fractional singular Sturm-Liouville problem. We show that the eigenvalues and eigenfunctions of the problem are real and orthogonal, respectively. Furthermore, we prove new approximations about the topic.

Sign in / Sign up

Export Citation Format

Share Document