Paper Info
Title
Higher-order Fourier Analysis and Applications.
Abstract
Fourier analysis has been extremely useful in many areas of mathematics. In the last several decades, it has been used extensively in theoretical computer science. Higher-order Fourier analysis is an extension of the classical Fourier analysis, where one allows to generalize the "linear phases" to higher degree polynomials. It has emerged from the seminal proof of Cowers of Szemeredi's theorem with improved quantitative bounds, and has been developed since, chiefly by the number theory community. In parallel, it has found applications also in theoretical computer science, mostly in algebraic property testing, coding theory and complexity theory. The purpose of this book is to lay the foundations of higher-order Fourier analysis, aimed towards applications in theoretical computer science with a focus on algebraic property testing.
Year
DOI
Venue
2019
10.1561/0400000064
FOUNDATIONS AND TRENDS IN THEORETICAL COMPUTER SCIENCE
Keywords
Field
DocType
Theoretical Computer Science,Computational complexity,Design and analysis of algorithms
Fourier analysis,Computational science,Mathematics,Computational complexity theory
Journal
Volume
Issue
ISSN
13
4
1551-305X
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Hamed Hatami121623.09
Pooya Hatami29414.40
Shachar Lovett352055.02