Displaying similar documents to “Balayage by Fourier transforms with sparse frequencies in compact abelian groups”

Pointwise convergence of the Fourier transform on locally compact abelian groups.

María L. Torres de Squire (1993)

Publicacions Matemàtiques

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We extend to locally compact abelian groups, Fejer's theorem on pointwise convergence of the Fourier transform. We prove that lim φ * f(y) = f (y) almost everywhere for any function f in the space (L, l)(G) (hence in L(G)), 2 ≤ p ≤ ∞, where {φ} is Simon's generalization to locally compact abelian groups of the summability Fejer Kernel. Using this result, we extend to locally compact abelian groups a theorem of F. Holland on the Fourier transform of unbounded measures of type q. ...

Sum-dominant sets and restricted-sum-dominant sets in finite abelian groups

David B. Penman, Matthew D. Wells (2014)

Acta Arithmetica

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We call a subset A of an abelian group G sum-dominant when |A+A| > |A-A|. If |A⨣A| > |A-A|, where A⨣A comprises the sums of distinct elements of A, we say A is restricted-sum-dominant. In this paper we classify the finite abelian groups according to whether or not they contain sum-dominant sets (respectively restricted-sum-dominant sets). We also consider how much larger the sumset can be than the difference set in this context. Finally, generalising work of Zhao, we provide asymptotic...

Inverse zero-sum problems in finite Abelian p-groups

Benjamin Girard (2010)

Colloquium Mathematicae

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We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible...