Functions with time and frequency gaps
type: Item
instance of: scholarly article
title: Functions with time and frequency gaps
zbMATH Open document ID: 0913.42007
author: O. Diekmann
published in: The Journal of Fourier Analysis and Applications
publication date: 1997-06-10T00:00:00Z
full work available at URL: https://eudml.org/doc/59498
review text: The purpose of this note is to give an explicit and straightforward construction of functions in \(L^1\cap C^\infty(\mathbb{R})\) that have prescribed gaps around the origin in both time and frequency domain. These gaps can be chosen independently and of arbitrary size. Moreover, the construction shows that the subspace of functions with these support properties is infinite-dimensional. An interesting additional feature of some examples is that they have periodic zero sets on both the time and the frequency domain.
Mathematics Subject Classification ID: 42A63
Mathematics Subject Classification ID: 46F12
zbMATH DE Number: 1019266
zbMATH Keywords: localization
zbMATH Keywords: spectral gaps
zbMATH Keywords: time and frequency domain
MaRDI profile type: Publication
OpenAlex ID: W2085324081
DOI: 10.1007/S00041-001-4046-Z
description: scientific article; zbMATH DE number 1019266