authors
- CASTILLO RODRIGUEZ, KENIER
- Ranga, Alagacone Sri
- Lamblem, Regina Litz
- Rafaeli, Fernando Rodrigo
Szego and Para-Orthogonal Polynomials On The Real Line: Zeros And Canonical Spectral Transformations
Articles
Overview
published in
- MATHEMATICS OF COMPUTATION Journal
publication date
- October 2012
start page
- 2229
end page
- 2249
volume
- 81
International Standard Serial Number (ISSN)
- 0025-5718
Electronic International Standard Serial Number (EISSN)
- 1088-6842
abstract
- 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.