שלחו לחבר

Salem conditions in the non-periodic case

Seminar
Speaker
Prof. E. Liflyand, Bar-Ilan University
Date
11/11/2019 - 15:30 - 14:00
Place
2nd floor Colloquium Room, Building 216
Abstract

In the classical sources, Salem's necessary conditions for a trigonometric series to be the Fourier 
series of an integrable function are given in terms of ``some" sums. Realizing that, in fact, they 
are given in terms of the discrete Hilbert transforms, we generalize these to the non-periodic case, 
for functions from the Wiener algebra. Other relations of the two objects are also discussed.
The obtained necessary condition is used to construct a monotone function with non-integrable cosine 
Fourier transform in a much easier way than in the classical book \cite{Ti} by Titchmarsh.
Certain open problems are posed.

תאריך עדכון אחרון : 11/11/2019