12. 3. 2024, od 9:00-9:45
Jaroslav Bradík, Sarason's product problem.
The seminar will take place in LVT1 (room no. 14)
12. 12. 2023, od 10:00-11:00
Miroslav Engliš, 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 Engliš, 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)