Program v akademickém roce 2023/2024


12. 12. 2023, od 10:00-11:00

Miroslav Englis, Positive-definite kernels and analytic contiuation.

The seminar will take place in Professor Smital's Library (room no.5)


14. 11. 2023, od 9:30-10:30

Miroslav Englis, M-harmonic functions and pseudodifferential operators.

The seminar will take place in Professor Smital's Library (room no.5)


31. 10. 2023, od 9:30-10:30

Petr Blaschke, A description of the boundary of a numerical range of a finite-dimensional matrix.

The seminar will take place in Professor Smital's Library (room no.5)


10. 10. 2023, od 9:30-10:30

Driss Aadi, Multiple sampling and Interpolation in standard weighted Bergman spaces of unit disk.

Abstract:
Sampling and interpolation sequences in space of analytic functions are among subjects widely studied in modern analysis for the last four decades, after Carleson's interpolation theorem. Besides, their theoretical considerations they find many applications concrete applications as in Gabor analysis signal processing, telecommunications, and etc. One of the most considerable work in space of analytic functions (after L. Carleson) goes back to K. Seip who completely characterized sampling and interpolation for both Bergman and Bargman-Fock space by mean of Landau type density tools around 1990's. Similarly to Hermite interpolation, a natural idea, is instead of looking at the values of a function not only at some samples (nodes) but also at its derivatives up to a certain order in the interpolation/sampling nodes. This leads to multiple interpolations/sampling. Actually, the same problem was considered in the case of Bargman-Fock space (resp. Hardy space only for interpolation) by Brekk and Seip (resp. Nikolski, Vasyunin, and Volberg others around 1970's). Recently, with Cruz, Hartman and Kellay, we were considering the situation of Bergman spaces of unit disk for which the underlying geometry is more intricate (pseudo-hyperbolic geometry). The main results obtained were a uniqueness condition through understanding a key hyperbolic radii for covering and separation, Also a necessary/sufficient condition in both the sampling and interpolation cases, with a small gap. We mention that our results may applied for bounded multiplicities, as a weak alternative for Seip's characterization of sampling/interpolation sequences (presence of a Beurling-Landau type densities, which are difficult to check in general, these results will be the subject of my talk, stemming from the paper \cite{ACHK} in https://doi.org/10.1016/j.jfa.2023.109865.

The seminar will take place in Professor Smital's Library (room no.5)