|Analysis Seminar in Crete (2021-22)|
Analysis Seminars in the World / Analysis seminars in Greece
|Wednesday, October 13, 2021||11:00||A303||Effie Papageorgiou||University of Crete||How many Fourier coefficients are needed?|
We are looking at families of functions or measures on the torus (in dimension one and two) which are specified by a finite number of parameters $N$. The task, for a given family, is to look at a small number of Fourier coefficients of the object, at a set of locations that is predetermined and may depend only on $N$, and determine the object. We look at (a) the indicator functions of at most $N$ intervals of the torus and (b) at sums of at most $N$ complex point masses on the two-dimensional torus. In the first case we reprove a theorem of Courtney which says that the Fourier coefficients at the locations $0, 1, \ldots, N$ are sufficient to determine the function (the intervals). In the second case we produce a set of locations of size $O(N \log N)$ which suffices to determine the measure.
Joint work with M. Kolountzakis (U. of Crete).
|Wednesday, October 27, 2021||11:00||A303||Nikos Karamanlis||University of Crete||Conformal maps in weighted Bergman spaces and the Bergman number|
|Abstract: We will give several geometric characterizations of conformal maps in weighted Bergman spaces. These characterizations involve certain conformal invariants, as well as certain Euclidean geometric quantities and they extend some known results for Hardy spaces to weighted Bergman spaces. Moreover, we shall discuss the notion of the Bergman number which is the analogue of the Hardy number for weighted Bergman spaces.|
|Wednesday, November 3, 2021||11:00||A303||Themis Mitsis||University of Crete||TBA|
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