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We introduce and study an inhomogeneous generalization of the spin -Whittaker polynomials from [15]. These are symmetric polynomials, and we prove a branching rule, skew dual and non-dual Cauchy identities, and an integral representation for them. Our main tool is a novel family of deformed Yang–Baxter equations.
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A Riemann–Hilbert approach to computing the inverse spectral map for measures supported on disjoint intervals
Abstract We develop a numerical method for computing with orthogonal polynomials that are orthogonal on multiple, disjoint intervals for which analytical formulae are currently unknown. Our approach exploits the Fokas–Its–Kitaev Riemann–Hilbert representation of the orthogonal polynomials to produce an method to compute the firstNrecurrence coefficients. The method can also be used for pointwise evaluation of the polynomials and their Cauchy transforms throughout the complex plane. The method encodes the singularity behavior of weight functions using weighted Cauchy integrals of Chebyshev polynomials. This greatly improves the efficiency of the method, outperforming other available techniques. We demonstrate the fast convergence of our method and present applications to integrable systems and approximation theory.
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- Award ID(s):
- 1945652
- PAR ID:
- 10441560
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Studies in Applied Mathematics
- Volume:
- 152
- Issue:
- 1
- ISSN:
- 0022-2526
- Format(s):
- Medium: X Size: p. 31-72
- Size(s):
- p. 31-72
- Sponsoring Org:
- National Science Foundation
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