Vol. 2, No. 4, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
ISSN (electronic): 2576-7666
ISSN (print): 2576-7658
Author Index
To Appear
 
Other MSP Journals
Trigonometric series with a given spectrum

Yves Meyer

Vol. 2 (2020), No. 4, 881–906
DOI: 10.2140/tunis.2020.2.881
Abstract

Let Λ n be a closed and discrete set. The vector space consisting of all trigonometric sums whose frequencies belong to Λ is denoted by TΛ. Given an exponent p [1,] we say that Λ is p-coherent if there exist a compact set K n and a continuous function ω defined on n with values in [1,) such that for every P TΛ and every y n one has (|xy|1|P(x)|pdx)1p ω(y)(K|P(x)|pdx)1p. Several properties of p-coherent sets are proved in this essay.

To the memory of Salah Baouendi

Keywords
mean periodic functions, almost periodic functions, trigonometric sums
Mathematical Subject Classification 2010
Primary: 42A32
Secondary: 42B10
Milestones
Received: 15 January 2019
Revised: 24 July 2019
Accepted: 7 August 2019
Published: 19 January 2020
Authors
Yves Meyer
CMLA, ENS-Cachan, CNRS, Université Paris-Saclay
France