Translator Disclaimer
2018 Orthogonal rational functions on the extended real line and analytic on the upper half plane
Xu Xu, Laiyi Zhu
Rocky Mountain J. Math. 48(3): 1019-1030 (2018). DOI: 10.1216/RMJ-2018-48-3-1019

Abstract

Let $\{\alpha _k\}_{k=1}^\infty$ be an arbitrary sequence of complex numbers in the upper half plane. We generalize the orthogonal rational functions $\phi _n$ based upon those points and obtain the Nevanlinna measure, together with the Riesz and Poisson kernels, for Caratheodory functions $F(z)$ on the upper half plane. Then, we study the relation between ORFs and their functions of the second kind as well as their interpolation properties. Further, by using a linear transformation, we generate a new class of rational functions and state the necessary conditions for guaranteeing their orthogonality.

Citation

Download Citation

Xu Xu. Laiyi Zhu. "Orthogonal rational functions on the extended real line and analytic on the upper half plane." Rocky Mountain J. Math. 48 (3) 1019 - 1030, 2018. https://doi.org/10.1216/RMJ-2018-48-3-1019

Information

Published: 2018
First available in Project Euclid: 2 August 2018

zbMATH: 06917361
MathSciNet: MR3835585
Digital Object Identifier: 10.1216/RMJ-2018-48-3-1019

Subjects:
Primary: 30C15, 30C20, 41A20, 42C05

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
12 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.48 • No. 3 • 2018
Back to Top