The problem of verifying the nonnegativity of a real valued function on a finite set is a long-standing challenging problem, which has received extensive attention from both mathematicians and computer scientists. Given a finite set $X$ together with a function $F:X \to \mathbb{R}$, if we equip $X$ a group structure $G$ via a bijection $\varphi:G \to X$, then effectively verifying the nonnegativity of $F$ on $X$ is equivalent to computing a sparse Fourier sum of squares (FSOS) certificate of $f=F\circ \varphi$ on $G$. In this paper, we show that by performing the fast (inverse) Fourier transform and finding a local minimal Fourier support, we are able to compute a sparse FSOS certificate of $f$ on $G$ with complexity $O(|G|\log |G| + |G| t^...
Abstract. We present a range of new results for testing properties of Boolean functions that are def...
AbstractClassical and recent results on uncertainty principles for functions on finite Abelian group...
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Fourier analysis expresses a function as a weighted sum of complex exponentials. The Fourier machine...
AbstractWe extend the theory of fast Fourier transforms on finite groups to finite inverse semigroup...
Many applications of machine learning on discrete domains, such as learning preference functions in ...
AbstractLet G be a finite group and f any complex-valued function defined on G and ϱ an irreducible ...
In this thesis we study the generalisation of Roth’s theorem on three term arithmetic progressions t...
Abstract. We present a range of new results for testing properties of Boolean functions that are def...
Let G be a finite group and f any complex-valued function defined on G and ae an irreducible comple...
Learning set functions is a key challenge arising in many domains, ranging from sketching graphs to ...
Higher-order Fourier analysis is a powerful tool that can be used to analyze the densities of linear...
AbstractIn this paper the complexity of computing the General Discrete Fourier Transform over group ...
This article reveals the basic techniques of fourier analysis on a finite abelian group .It may be u...
The arithmetic regularity lemma due to Green [GAFA 2005] is an analogue of the famous Szemerédi regu...
Abstract. We present a range of new results for testing properties of Boolean functions that are def...
AbstractClassical and recent results on uncertainty principles for functions on finite Abelian group...
AbstractThis paper presents a new algorithm for constructing a complete list of pairwise inequivalen...
Fourier analysis expresses a function as a weighted sum of complex exponentials. The Fourier machine...
AbstractWe extend the theory of fast Fourier transforms on finite groups to finite inverse semigroup...
Many applications of machine learning on discrete domains, such as learning preference functions in ...
AbstractLet G be a finite group and f any complex-valued function defined on G and ϱ an irreducible ...
In this thesis we study the generalisation of Roth’s theorem on three term arithmetic progressions t...
Abstract. We present a range of new results for testing properties of Boolean functions that are def...
Let G be a finite group and f any complex-valued function defined on G and ae an irreducible comple...
Learning set functions is a key challenge arising in many domains, ranging from sketching graphs to ...
Higher-order Fourier analysis is a powerful tool that can be used to analyze the densities of linear...
AbstractIn this paper the complexity of computing the General Discrete Fourier Transform over group ...
This article reveals the basic techniques of fourier analysis on a finite abelian group .It may be u...
The arithmetic regularity lemma due to Green [GAFA 2005] is an analogue of the famous Szemerédi regu...
Abstract. We present a range of new results for testing properties of Boolean functions that are def...
AbstractClassical and recent results on uncertainty principles for functions on finite Abelian group...
AbstractThis paper presents a new algorithm for constructing a complete list of pairwise inequivalen...