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

Wednesday, December 8, 2021, 11:00, Room: A303
Speaker: Mihalis Kolountzakis (University of Crete)

The size of a common tile of several lattices

Abstract:

Old and new results will be described on the following question: if $T$ is a common set of coset representatives for the subgroups $G_i$ of the abelian group $G$, all of them of the same index, how large must $T$ be? This will be discussed under various assumptions and several notions of what it means to be large.

The $G_i$ are mostly lattices in Euclidean spaces, and $T$ is mostly assumed to be measurable, but not always. Several open questions, of varying levels of difficulty will be presented.

Wednesday, January 12, 2022, 11:00, Room: A303
Speaker: Nikos Karamanlis (University of Crete)

A characterization of the unit disk and the harmonic measure doubling condition

Abstract: Suppose $D$ is a bounded Jordan domain in the plane. A well known theorem by Jerison and Kenig states that the boundary of $D$ is a quasicircle if and only if both $D$ and its complement are doubling domains with respect to the harmonic measure. This theorem fails if we only assume that $D$ is a doubling domain. We show that if $D$ is a doubling domain with constant $c = 1$, then it must be a disk.

All seminars

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