Orthogonal polynomials in the complex plane and on the real line

1997 ◽  
pp. 211-245 ◽  
Author(s):  
Walter Van Assche
Keyword(s):  
Orthogonal Polynomials ◽  
Complex Plane ◽  
Real Line ◽  
The Real

scholarly journals Sylvester equations for Laguerre–Hahn orthogonal polynomials on the real line

2013 ◽  
Vol 219 (17) ◽  
pp. 9118-9131 ◽  
Author(s):  
A. Branquinho ◽  
A. Paiva ◽  
M.N. Rebocho
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
The Real

scholarly journals LOWERING AND RAISING OPERATORS FOR THE FREE MEIXNER CLASS OF ORTHOGONAL POLYNOMIALS

2009 ◽  
Vol 12 (03) ◽  
pp. 387-399 ◽  
Author(s):  
EUGENE LYTVYNOV ◽  
IRINA RODIONOVA
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
Meixner Polynomials ◽  
The Real ◽  
Raising Operators ◽  
Meixner Class

We compare some properties of the lowering and raising operators for the classical and free classes of Meixner polynomials on the real line.

scholarly journals New Stability Criteria for Discrete Linear Systems Based on Orthogonal Polynomials

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1322
Author(s):  
Luis E. Garza ◽  
Noé Martínez ◽  
Gerardo Romero
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Linear Systems ◽  
Real Line ◽  
Stability Criteria ◽  
The Real ◽  
Discrete Linear Systems ◽  
New Criterion ◽  
Schur Stability

A new criterion for Schur stability is derived by using basic results of the theory of orthogonal polynomials. In particular, we use the relation between orthogonal polynomials on the real line and on the unit circle known as the Szegő transformation. Some examples are presented.

scholarly journals Delange's characterization of the sine function

1974 ◽  
Vol 15 (1) ◽  
pp. 66-68 ◽  
Author(s):  
Chin-Hung Ching ◽  
Charles K. Chui
Keyword(s):  
Entire Function ◽  
Analytic Continuation ◽  
Complex Plane ◽  
Real Line ◽  
Sine Function ◽  
The Real ◽  
Image Position

In [2], H. Delange gives the following characterization of the sine function.Theorem A. f(x)=sin x is the only infinitely differentiable real-valued function on the real line such that f'(O)= 1 andfor all real x and n = 0,1,2,….It is clear that, if f satisfies (1), then the analytic continuation of f is an entire function satisfyingfor all z in the complex plane. Hence f is of at most order one and type one. In this note, we prove the following theorem.

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