Bernd Beckermann - Bergman orthogonal polynomials and the Grunsky matrix
20 December 2018 –
By exploiting a link between Bergman orthogonal polynomials and the Grunsky matrix, probably first observed by Kühnau in 1985, we improve on some recent results on strong asymptotics of Bergman polynomials outside the domain G of orthogonality, and on the entries of the Bergman shift operator. In our proofs we suggest a new matrix approach involving the Grunsky matrix, and use well-established results in the literature relating properties of the Grunsky matrix to the regularity of the boundary of G and the associated conformal maps. For quasiconformal boundaries this approach allows for new insights for Bergman polynomials.
Joint work with Nikos Stylianopoulos (Nicosie). For more details see https://arxiv.org/pdf/1606.00553.pdf
Bernhard Beckermann, Professor, Université de Lille.