scholarly journals Higher-order Fourier Analysis and Applications

2019 ◽  
Vol 13 (4) ◽  
pp. 247-448
Author(s):  
Hamed Hatami ◽  
Pooya Hatami ◽  
Shachar Lovett

2016 ◽  
Vol 30 (1) ◽  
pp. 67-157 ◽  
Author(s):  
Nikos Frantzikinakis ◽  
Bernard Host


2009 ◽  
Vol 31 (1) ◽  
pp. 113-142 ◽  
Author(s):  
BERNARD HOST ◽  
BRYNA KRA

AbstractWe study relations between subsets of integers that are large, where large can be interpreted in terms of size (such as a set of positive upper density or a set with bounded gaps) or in terms of additive structure (such as a Bohr set). Bohr sets are fundamentally abelian in nature and are linked to Fourier analysis. Recently it has become apparent that a higher order, non-abelian, Fourier analysis plays a role both in additive combinatorics and in ergodic theory. Here we introduce a higher-order version of Bohr sets and give various properties of these objects, generalizing results of Bergelson, Furstenberg, and Weiss.



10.37236/4445 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Hamed Hatami ◽  
Pooya Hatami ◽  
James Hirst

We study sequences of functions of the form $\mathbb{F}_p^n \to \{0,1\}$ for varying $n$, and define a notion of convergence based on the induced distributions from restricting the functions to a random affine subspace. Using a decomposition theorem   and a recently proven equi-distribution theorem from higher order Fourier analysis, we prove that the limits of such convergent sequences can be represented by certain measurable functions.  We also show that every such limit object arises as the limit of some sequence of functions. These results are in the spirit of similar results which have been developed for limits of graph sequences. A more general, albeit substantially more sophisticated, limit object was recently constructed by Balázs Szegedy [Gowers norms, regularization and limits of functions on abelian groups. 2010. arXiv:1010.6211].



2019 ◽  
Author(s):  
Hamed Hatami ◽  
Pooya Hatami ◽  
Shachar Lovett


2012 ◽  
Vol 46 (21) ◽  
pp. 2675-2694 ◽  
Author(s):  
Ahmet Sinan Oktem ◽  
C Guedes Soares


PIERS Online ◽  
2006 ◽  
Vol 2 (4) ◽  
pp. 409-411
Author(s):  
Dirk K. Callebaut ◽  
Geoffrey K. Karugila ◽  
Ahmed. H. Khater


2012 ◽  
Author(s):  
Terence Tao




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