Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Orthogonal polynomials on several intervals via a polynomial mapping


Authors: J. S. Geronimo and W. Van Assche
Journal: Trans. Amer. Math. Soc. 308 (1988), 559-581
MSC: Primary 42C05; Secondary 30E05, 33A65
DOI: https://doi.org/10.1090/S0002-9947-1988-0951620-6
MathSciNet review: 951620
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Starting from a sequence $\{ {p_n}(x; {\mu _0})\}$ of orthogonal polynomials with an orthogonality measure ${\mu _0}$ supported on ${E_0} \subset [ - 1, 1]$, we construct a new sequence $\{ {p_n}(x; \mu )\}$ of orthogonal polynomials on $E = {T^{ - 1}}({E_0})$ ($T$ is a polynomial of degree $N$) with an orthogonality measure $\mu$ that is related to ${\mu _0}$. If ${E_0} = [ - 1, 1]$, then $E = {T^{ - 1}}([ - 1, 1])$ will in general consist of $N$ intervals. We give explicit formulas relating $\{ {p_n}(x; \mu )\}$ and $\{ {p_n}(x; {\mu _0})\}$ and show how the recurrence coefficients in the three-term recurrence formulas for these orthogonal polynomials are related. If one chooses $T$ to be a Chebyshev polynomial of the first kind, then one gets sieved orthogonal polynomials.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42C05, 30E05, 33A65

Retrieve articles in all journals with MSC: 42C05, 30E05, 33A65


Additional Information

Keywords: Orthogonal polynomials, recurrence coefficients, Jacobi matrices
Article copyright: © Copyright 1988 American Mathematical Society