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Title: Complex exceptional orthogonal polynomials and quasi-invariance
Authors: Haese-Hill, William
Veselov, A.P.
Hallnas, Martin
Issue Date: 2016
Publisher: © Springer Verlag (Germany)
Citation: HAESE-HILL, W., VESELOV, A.P. and HALLNAS, M., 2016. Complex exceptional orthogonal polynomials and quasi-invariance. Letters in Mathematical Physics, 106(5), pp.583-606.
Abstract: Consider the Wronskians of the classical Hermite polynomials Hλ₁(x):= Wr(Hl(x);Hk1 (x)…;Hkn(x)); l ϵ Z≥0 \{k1; : : : ; kn}; where ki = λ₁ + n - i; i = 1;…, n and λ = (λ₁;…; λn) is a partition. Gómez-Ullate et al. showed that for a special class of partitions the corresponding polynomials are orthogonal and dense among all polynomials with respect to a certain inner product, but in contrast to the usual case have some degrees missing (so called exceptional orthogonal polynomials). We generalise their results to all partitions by considering complex contours of integration and non-positive Hermitian products. The corresponding polynomials are orthogonal and dense in a finite-codimensional subspace of C[x] satisfying certain quasi-invariance conditions. A Laurent version of exceptional orthogonal polynomials, related to monodromy-free trigonometric Schrödinger operators, is also presented.
Description: This is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/
Version: Published
DOI: 10.1007/s11005-016-0828-8
URI: https://dspace.lboro.ac.uk/2134/20349
Publisher Link: http://dx.doi.org/10.1007/s11005-016-0828-8
ISSN: 1573-0530
Appears in Collections:Published Articles (Maths)

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