## Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I

Publication
, Journal Article

McLaughlin, KTR; Vartanian, AH; Zhou, X

Published in: Mathematical Physics Analysis and Geometry

November 1, 2008

Orthogonal rational functions are characterized in terms of a family of matrix Riemann-Hilbert problems on ℝ, and a related family of energy minimisation problems is presented. Existence, uniqueness, and regularity properties of the equilibrium measures which solve the energy minimisation problems are established. These measures are used to derive a family of 'model' matrix Riemann-Hilbert problems which are amenable to asymptotic analysis via the Deift-Zhou non-linear steepest-descent method. © 2008 Springer Science+Business Media B.V.

### Duke Scholars

## Published In

Mathematical Physics Analysis and Geometry

## DOI

## ISSN

1385-0172

## Publication Date

November 1, 2008

## Volume

11

## Issue

3-4

## Start / End Page

187 / 364

## Related Subject Headings

- General Mathematics
- 02 Physical Sciences
- 01 Mathematical Sciences

### Citation

APA

Chicago

ICMJE

MLA

NLM

McLaughlin, K. T. R., Vartanian, A. H., & Zhou, X. (2008). Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I.

*Mathematical Physics Analysis and Geometry*,*11*(3–4), 187–364. https://doi.org/10.1007/s11040-008-9042-yMcLaughlin, K. T. R., A. H. Vartanian, and X. Zhou. “Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I.”

*Mathematical Physics Analysis and Geometry*11, no. 3–4 (November 1, 2008): 187–364. https://doi.org/10.1007/s11040-008-9042-y.McLaughlin KTR, Vartanian AH, Zhou X. Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I. Mathematical Physics Analysis and Geometry. 2008 Nov 1;11(3–4):187–364.

McLaughlin, K. T. R., et al. “Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I.”

*Mathematical Physics Analysis and Geometry*, vol. 11, no. 3–4, Nov. 2008, pp. 187–364.*Scopus*, doi:10.1007/s11040-008-9042-y.McLaughlin KTR, Vartanian AH, Zhou X. Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I. Mathematical Physics Analysis and Geometry. 2008 Nov 1;11(3–4):187–364.

## Published In

Mathematical Physics Analysis and Geometry

## DOI

## ISSN

1385-0172

## Publication Date

November 1, 2008

## Volume

11

## Issue

3-4

## Start / End Page

187 / 364

## Related Subject Headings

- General Mathematics
- 02 Physical Sciences
- 01 Mathematical Sciences