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math.CA2026
The and Bi-orthogonal Polynomials on the Unit Circle: Further Properties and Riemann-Hilbert Characterizations
Roozbeh Gharakhloo, Nicholas S. Witte
In previous work \cite{GW}, we developed a theory of modulated \(2j-k\) bi-orthogonal polynomial systems \(\{P_n(z;r),Q_n(z;r)\}\) and \(j-2k\) bi-orthogonal polynomial systems \(\…
math.CA2026
Reduction of Multiple Orthogonal Polynomials to Standard Orthogonal Polynomials
Roozbeh Gharakhloo, Maksim Kosmakov, Kenta Miyahara
In this article, we derive explicit formulae expressing multiple orthogonal polynomials in terms of standard orthogonal polynomials. We treat both the real-line and unit-circle set…