Spectral analysis of indefinite Sturm-Liouville operators

2014 ◽  
Vol 48 (3) ◽  
pp. 227-230
Author(s):  
A. S. Kostenko
Keyword(s):  
Spectral Analysis ◽  
Sturm Liouville ◽  
Liouville Operators

scholarly journals Spectral analysis of singular Sturm-Liouville operators on time scales

2018 ◽  
Vol 72 (1) ◽  
pp. 1 ◽  
Author(s):  
Bilender P. Allahverdiev ◽  
Huseyin Tuna
Keyword(s):  
Spectral Analysis ◽  
Continuous Spectrum ◽  
Discrete Spectrum ◽  
Time Scales ◽  
Liouville Operator ◽  
Adjoint Operator ◽  
The Self ◽  
Sturm Liouville ◽  
Liouville Operators

In this paper, we consider properties of the spectrum of a Sturm-Liouville<br />operator on time scales. We will prove that the regular symmetric<br />Sturm-Liouville operator is semi-bounded from below. We will also give some<br />conditions for the self-adjoint operator associated with the singular<br />Sturm-Liouville expression to have a discrete spectrum. Finally, we will<br />investigate the continuous spectrum of this operator.

Spectral analysis of dissipative fractional Sturm–Liouville operators

2017 ◽  
Vol 24 (3) ◽  
pp. 351-362
Author(s):  
Aytekin Eryılmaz ◽  
Hüseyin Tuna
Keyword(s):  
Spectral Analysis ◽  
Fractional Calculus ◽  
Sturm Liouville ◽  
Liouville Operators

AbstractWe study fractional Sturm–Liouville operators. We give some basic definitions and properties of fractional calculus. Using the method of Pavlov [31, 30, 32], we prove a theorem on the completeness of the system of eigenvectors and associated vectors of dissipative fractional Sturm–Liouville operators.

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