Analysis Seminar in Crete (2021-22)

Σεμιναριο Αναλυσης

In chronological ordering

Wednesday, October 13, 2021, 11:00, Room: A303
Speaker: Effie Papageorgiou (University of Crete)

How many Fourier coefficients are needed?

Abstract:

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, Room: A303
Speaker: 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, Room: A303
Speaker: Themis Mitsis (University of Crete)

A geometric approach to the distance-set problem

Abstract: In the problem of the distance set we are seeking a lower bound for the "size" of the set of all distances between points of a set $A$ as a function of the "size" of the set $A$. While all approaches are using the Fourier Transform, I will describe a naive geometric method, which, without giving optimal results, can give non-trivial information.

Wednesday, November 10, 2021, 11:00, Room: A303
Speaker: Camille Labourie (University of Cyprus)

Calibrations for a free-discontinuity problem with Robin condition

Abstract: Here

All seminars

Page maintained by Mihalis Kolountzakis, Nikos Frantzikinakis, Mihalis Papadimitrakis