Balayage by Fourier transforms with sparse frequencies in compact abelian groups
George S. Shapiro (1981)
Colloquium Mathematicae
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George S. Shapiro (1981)
Colloquium Mathematicae
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Hewitt, E.
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Kathryn E. Hare (1988)
Colloquium Mathematicae
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J. Florek (1987)
Colloquium Mathematicae
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Nemzer, Dennis (1994)
International Journal of Mathematics and Mathematical Sciences
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Sergey Avgustinovich, Juhani Karhumäki, Svetlana Puzynina (2012)
RAIRO - Theoretical Informatics and Applications
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In the paper we study abelian versions of the critical factorization theorem. We investigate both similarities and differences between the abelian powers and the usual powers. The results we obtained show that the constraints for abelian powers implying periodicity should be quite strong, but still natural analogies exist.
McKennon, Kelly (1982)
International Journal of Mathematics and Mathematical Sciences
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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. ...