Spectral theory of semibounded Sturm–Liouville operators with local interactions on a discrete set

2010 ◽  
Vol 51 (10) ◽  
pp. 102102 ◽  
Author(s):  
Sergio Albeverio ◽  
Aleksey Kostenko ◽  
Mark Malamud
Keyword(s):  
Spectral Theory ◽  
Local Interactions ◽  
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.

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