XXXVII Workshop on Geometric Methods in Physics | 1-7.07.2018 |

VII School on Geometry and Physics | 25-29.06.2018 |

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## Tommasz Łukasz Żynda## Weighted generalization of the Szeg\"o kernel and its dependence on the weight of integrationA concept of reproducing kernel is connected with a Hilbert space. Not for every Hilbert space, however, there exists a reproducing kernel of it. An example of such weighted Bergman space gave Z. Pasternak-Winiarski in [1]. In that paper, he gave a characterization theorem for weights of integration (which he called admissible weights), for which there exists a reproducing kernel of the corresponding weighted Bergman space. The aim of this presentation is to answer the question for which weights of integration there exists a reproducing kernel of the weighted Szeg\"o space and how does the weighted Szeg\"o kernel depend on the weight of integration. The talk will be partially based on [2]. [1] Z. Pasternak-Winiarski, "On weights which admit the reproducing kernel of Bergman type", Internation Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 1, p. 1-14 (1992). [2] Z. Pasternak-Winiarski, T. Ł. Żynda, "Weighted Szeg\"o Kernels", Geometric Methods in Physics XXXV, p. 151-157 (2018). |

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