Asymptotics of derivatives of orthogonal polynomials on the real line

E. Levin; D. S. Lubinsky

doi:10.1007/s10474-007-6183-6

Asymptotics of derivatives of orthogonal polynomials on the real line

E. Levin, D. S. Lubinsky

Mathematics discipline

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

Abstract

We show that uniform asymptotics of orthogonal polynomials on the real line imply uniform asymptotics for all their derivatives. This is more technically challenging than the corresponding problem on the unit circle. We also examine asymptotics in the L ₂ norm.

Original language	English
Pages (from-to)	115-127
Number of pages	13
Journal	Acta Mathematica Hungarica
Volume	118
Issue number	1-2
DOIs	https://doi.org/10.1007/s10474-007-6183-6
State	Published - Jan 2008

Bibliographical note

Funding Information:
∗Research supported by NSF grant DMS0400446 and US-Israel BSF grant 2004353. Key words and phrases: derivatives of orthogonal polynomials, asymptotics of orthogonal polynomials, Szeg®'s condition. 2000 Mathematics Subject Classification: primary 42C05, 42C99, secondary 41A60.

Keywords

Asymptotics of orthogonal polynomials
Derivatives of orthogonal polynomials
Szego's condition

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10.1007/s10474-007-6183-6

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abstract = "We show that uniform asymptotics of orthogonal polynomials on the real line imply uniform asymptotics for all their derivatives. This is more technically challenging than the corresponding problem on the unit circle. We also examine asymptotics in the L 2 norm.",

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KW - Szego's condition

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Asymptotics of derivatives of orthogonal polynomials on the real line

Abstract

Bibliographical note

Keywords

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