A Survey on Markov’s Theorem on Zeros of Orthogonal Polynomials

2020 ◽  
pp. 23-50
Author(s):  
Kenier Castillo ◽  
Marisa de Souza Costa ◽  
Fernando Rodrigo Rafaeli
Keyword(s):  
Orthogonal Polynomials ◽  
Zeros Of Orthogonal Polynomials

Convolutions and zeros of orthogonal polynomials

2011 ◽  
Vol 61 (7) ◽  
pp. 868-878
Author(s):  
Iván Area ◽  
Dimitar K. Dimitrov ◽  
Eduardo Godoy
Keyword(s):  
Orthogonal Polynomials ◽  
Zeros Of Orthogonal Polynomials

scholarly journals Interlacing of zeros of orthogonal polynomials under modification of the measure

2013 ◽  
Vol 175 ◽  
pp. 64-76 ◽  
Author(s):  
Dimitar K. Dimitrov ◽  
Mourad E.H. Ismail ◽  
Fernando R. Rafaeli
Keyword(s):  
Orthogonal Polynomials ◽  
Interlacing Of Zeros ◽  
Zeros Of Orthogonal Polynomials

Mean Convergence of Lagrange Interpolation for Exponential weights on [-1, 1]

1998 ◽  
Vol 50 (6) ◽  
pp. 1273-1297 ◽  
Author(s):  
D. S. Lubinsky
Keyword(s):  
Orthogonal Polynomials ◽  
Lagrange Interpolation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Exponential Weights ◽  
Mean Convergence ◽  
Zeros Of Orthogonal Polynomials ◽  
Necessary And Sufficient

AbstractWe obtain necessary and sufficient conditions for mean convergence of Lagrange interpolation at zeros of orthogonal polynomials for weights on [-1, 1], such asw(x) = exp(-(1 - x2)-α), α > 0orw(x) = exp(-expk(1 - x2)-α), k≥1, α > 0,where expk = exp(exp(. . . exp( ) . . .)) denotes the k-th iterated exponential.

scholarly journals Interpolatory product integration for Riemann-integrable functions

1987 ◽  
Vol 29 (2) ◽  
pp. 195-202 ◽  
Author(s):  
Philip Rabinowitz ◽  
William E. Smith
Keyword(s):  
Orthogonal Polynomials ◽  
Integration Interval ◽  
Product Integration ◽  
Zeros Of Orthogonal Polynomials ◽  
Integrable Functions ◽  
Riemann Integrable Functions ◽  
Integration Rules

AbstractConditions are fround for the convergence of intepolatory product integration rules and the corresponding companion rules for the class of Riemann-integrable functions. These condtions are used to prove convergence for several classes of rules based on sets of zeros of orthogonal polynomials possibly augmented by one both of the endpoints of the integration interval.

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