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
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
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