scholarly journals Nonself-Adjoint Second-Order Difference Operators in Limit-Circle Cases

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Bilender P. Allahverdiev
Keyword(s):  
Second Order ◽  
Difference Operators ◽  
Order Difference ◽  
Limit Circle

Structure of fractional spaces generated by second order difference operators

2014 ◽  
Vol 351 (2) ◽  
pp. 713-731 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Neşe Nalbant ◽  
Yaşar Sözen
Keyword(s):  
Second Order ◽  
Difference Operators ◽  
Order Difference ◽  
Fractional Spaces

Non-self-adjoint difference operators and their spectrum

2005 ◽  
Vol 461 (2057) ◽  
pp. 1505-1531 ◽  
Author(s):  
Robert Howard Wilson
Keyword(s):  
Difference Operator ◽  
Discrete Analogue ◽  
Second Order ◽  
Difference Operators ◽  
Essential Difference ◽  
Order Difference ◽  
Second Order Differential Equations ◽  
Forward Difference ◽  
Difference Expression ◽  
Complex Coefficients

Initially, this paper is a discrete analogue of the work of Brown et al. (1999 Proc. R. Soc. A 455 , 1235–1257) on second-order differential equations with complex coefficients. That is, we investigate the general non-self-adjoint second-order difference expression where the coefficients p n and q n are complex and Δ is the forward difference operator, i.e. Δ x n = x n +1 − x n . Properties of the so-called Hellinger–Nevanlinna m -function for the recurrence relation Mx n = λ w n x n , where the w n are real and positive, are examined, and relationships between the properties of the m -function and the spectrum of the associated operator are explored. However, an essential difference between the continuous and the discrete case arises in the way in which we define the operator natural to the problem. Nevertheless, analogous results regarding the spectrum of this operator are obtained.

Spectral problems of nonself-adjoint singular discrete Sturm-Liouville operators

2016 ◽  
Vol 66 (4) ◽  
Author(s):  
Bilender P. Allahverdiev
Keyword(s):  
Difference Operators ◽  
Boundary Values ◽  
Defect Index ◽  
Order Difference ◽  
Limit Circle ◽  
Limit Circle Case ◽  
Sturm Liouville ◽  
Limit Point Case ◽  
Circle Case ◽  
Liouville Operators

AbstractIn this study we construct a space of boundary values of the minimal symmetric discrete Sturm-Liouville (or second-order difference) operators with defect index (1, 1) (in limit-circle case at ±∞ and limit-point case at ∓∞), acting in the Hilbert space

Sign in / Sign up

Export Citation Format

Share Document