Remarks on the box problem
type: Item
instance of: scholarly article
title: Remarks on the box problem
zbMATH Open document ID: 1031.42018
author: Nets Hawk Katz
author: Elliot Krop
author: Mauro Maggioni
published in: Mathematical Research Letters
publication date: 2004-03-07T00:00:00Z
review text: In connection with the study of Fourier integral operators there arises the question for an upper bound of the measure of the set \[ S= \{x\in Q:|f(x)|< 1\}, \] where \(Q\) is the unit cube and \(f\) is a \(C^n\) function on \(Q\) satisfying \(\partial^n_{x_1x_2\cdots x_n}f>\Lambda\). Related to this question the authors define a (CCW)-condition to given sets. They have an upper bound and a lower bound for \(|S|\) in the form \(O(\Lambda^{2^{1-n}})\) and \(O(\Lambda^{n^{-1}})\). Finally, they study a discrete analogue of the above question. This question was stated by Erdős in the context of hypergraphs.
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 35S30
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 1886046
zbMATH Keywords: box problem
zbMATH Keywords: Fourier integral operators
zbMATH Keywords: hypergraphs
reviewed by: Michael Reissig
MaRDI profile type: Publication
full work available at URL: mrl.2002.v9.n4.a11
OpenAlex ID: W1998632521
DOI: 10.4310/MRL.2002.V9.N4.A11
description: scientific article; zbMATH DE number 1886046