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Martin Hallnäs (Chalmers University of Technology and University of Gothenburg): Exceptional orthogonal polynomials and quasi-invariance

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Tuesday, 8. May 2018, 10:00 - 11:00
Abstract. The focus of my talk will be on systems of polynomials given in terms of Wronskians of classical Hermite polynomials and naturally labelled by partitions.

For the special class of so-called double partitions, Gomez-Ullate, Grandati and Milson showed that the corresponding polynomials are orthogonal and dense in the space of all polynomials with respect to a certain inner product, but in contrast to their classical counterparts have some degrees missing (so-called exceptional orthogonal polynomials). I will describe how their results can be generalised to all partitions by using the notion of quasi-invariance and considering complex contours of integration and non-positive, but Hermitian, inner products.

If time permits, I will also indicate a multivariate generalisation of some of these results. The talk is based on joint work with W.A. Haese-Hill and A.P. Veselov.
Location : Bolyai Intézet, II. emelet, Rédei terem, Aradi Vértanúk tere 1., Szeged


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