Orthogonal polynomials for weights close to indeterminacy

E. Levin; D. S. Lubinsky

doi:10.1016/j.jat.2007.01.001

Orthogonal polynomials for weights close to indeterminacy

E. Levin, D. S. Lubinsky

Mathematics discipline

Research output: Contribution to journal › Article › peer-review

Abstract

We obtain estimates for Christoffel functions and orthogonal polynomials for even weights W : R → [0, ∞) that are 'close' to indeterminate weights. Our main example is exp fenced(- || fenced(x) fenced(log || fenced(x))^β), with β real, possibly modified near 0, but our results also apply to exp fenced(- || fenced(x)^α fenced(log || fenced(x))^β), α < 1. These types of weights exhibit interesting properties largely because they are either indeterminate or are close to the border between determinacy and indeterminacy in the classical moment problem.

Original language	English
Pages (from-to)	129-168
Number of pages	40
Journal	Journal of Approximation Theory
Volume	147
Issue number	2
DOIs	https://doi.org/10.1016/j.jat.2007.01.001
State	Published - Aug 2007

Bibliographical note

Funding Information:
Research supported by NSF Grant DMS 0400446 and US-Israel BSF Grant 2004353. ∗ Corresponding author. Fax: +1 404 894 4409. E-mail addresses: [email protected] (E. Levin), [email protected] (D.S. Lubinsky).

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abstract = "We obtain estimates for Christoffel functions and orthogonal polynomials for even weights W : R → [0, ∞) that are 'close' to indeterminate weights. Our main example is exp fenced(- || fenced(x) fenced(log || fenced(x))β), with β real, possibly modified near 0, but our results also apply to exp fenced(- || fenced(x)α fenced(log || fenced(x))β), α < 1. These types of weights exhibit interesting properties largely because they are either indeterminate or are close to the border between determinacy and indeterminacy in the classical moment problem.",

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N2 - We obtain estimates for Christoffel functions and orthogonal polynomials for even weights W : R → [0, ∞) that are 'close' to indeterminate weights. Our main example is exp fenced(- || fenced(x) fenced(log || fenced(x))β), with β real, possibly modified near 0, but our results also apply to exp fenced(- || fenced(x)α fenced(log || fenced(x))β), α < 1. These types of weights exhibit interesting properties largely because they are either indeterminate or are close to the border between determinacy and indeterminacy in the classical moment problem.

AB - We obtain estimates for Christoffel functions and orthogonal polynomials for even weights W : R → [0, ∞) that are 'close' to indeterminate weights. Our main example is exp fenced(- || fenced(x) fenced(log || fenced(x))β), with β real, possibly modified near 0, but our results also apply to exp fenced(- || fenced(x)α fenced(log || fenced(x))β), α < 1. These types of weights exhibit interesting properties largely because they are either indeterminate or are close to the border between determinacy and indeterminacy in the classical moment problem.

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ER -

Orthogonal polynomials for weights close to indeterminacy

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