The Diagonal of the Padé Table and the Approximation of the Weyl Function of Second-Order Difference Operators

1997 ◽  
Vol 13 (4) ◽  
pp. 481-510 ◽  
Author(s):  
B. Beckermann ◽  
V. Kaliaguine
Keyword(s):  
Weyl Function ◽  
Second Order ◽  
Difference Operators ◽  
Order Difference

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.

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