Interpolation sets and arithmetic progressions

Series: 
Analysis Seminar
Wednesday, February 8, 2017 - 14:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Tel-Aviv University
Organizer: 
Given a set S of positive measure on the unit circle, a set of integers K is an interpolation set (IS) for S if for any data {c(k)} in l^2(K) there exists a function f in L^2(S) such that its Fourier coefficients satisfy f^(k)=c(k) for all k in K.  In the talk I will discuss the relationship between the concept of IS and the existence of arbitrarily long arithmetic progressions with specified lengths and step sizes in K. Multidimensional analogues of this subject will also be considered.This talk is based on joint work with Alexander Olevskii.