Counterexamples in the spectral theory of singular Sturm — Liouville operators

1974 ◽  
pp. 373-382 ◽  
Author(s):  
S. G. Halvorsen
Keyword(s):  
Spectral Theory ◽  
Sturm Liouville ◽  
Liouville Operators

Spectral theory of dissipative q-Sturm-Liouville problems

2014 ◽  
Vol 51 (3) ◽  
pp. 366-383
Author(s):  
Aytekin Eryilmaz ◽  
Hüseyin Tuna
Keyword(s):  
Hilbert Space ◽  
Characteristic Function ◽  
Spectral Theory ◽  
Difference Operator ◽  
Functional Model ◽  
Dissipative Operator ◽  
Eigenvalues And Eigenvectors ◽  
Maximal Dissipative Operator ◽  
Sturm Liouville ◽  
Liouville Operators

This paper is devoted to studying a q-analogue of Sturm-Liouville operators. We formulate a dissipative q-difference operator in a Hilbert space. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which is based on the method of Pavlov and define its characteristic function. Finally, we prove theorems on the completeness of the system of eigenvalues and eigenvectors of the maximal dissipative q-Sturm-Liouville difference operator.

scholarly journals Inverse spectral theory for Sturm-Liouville operators with distributional potentials

2013 ◽  
Vol 88 (3) ◽  
pp. 801-828 ◽  
Author(s):  
Jonathan Eckhardt ◽  
Fritz Gesztesy ◽  
Roger Nichols ◽  
Gerald Teschl
Keyword(s):  
Spectral Theory ◽  
Inverse Spectral Theory ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Liouville Operators
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