SZEGO and PARA-ORTHOGONAL POLYNOMIALS on THE REAL LINE: ZEROS and CANONICAL SPECTRAL TRANSFORMATIONS
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Data
2012-10-01
Autores
Castillo, Kenier [UNESP]
Lamblem, Regina Litz
Rafaeli, Fernando Rodrigo [UNESP]
Ranga, Alagacone Sri [UNESP]
Título da Revista
ISSN da Revista
Título de Volume
Editor
Amer Mathematical Soc
Resumo
We study polynomials which satisfy the same recurrence relation as the Szego polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szego polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szego polynomials, para-orthogonal polynomials and associated quadrature rules are also studied. Finally, again with positive values for the reflection coefficients, interlacing properties of the Szego polynomials and polynomials arising from canonical spectral transformations are obtained.
Descrição
Palavras-chave
Szegö polynomials, Para-orthogonal polynomials, reflection coefficients, canonical spectral transformations
Como citar
Mathematics of Computation. Providence: Amer Mathematical Soc, v. 81, n. 280, p. 2229-2249, 2012.