(,) mapping properties of convolution transforms
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G. Sampson, A. Naparstek, V. Drobot (1976)
Studia Mathematica
Jansche, Stefan (1997)
Journal of Inequalities and Applications [electronic only]
František Štěpánek (2004)
Pokroky matematiky, fyziky a astronomie
František Štěpánek (2004)
Pokroky matematiky, fyziky a astronomie
A. Zygmund (1972)
Studia Mathematica
G.T. LaVarnway, R. Cooke (2001)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
Philippe Jaming (2010)
Colloquium Mathematicae
The aim of this paper is to show that, in various situations, the only continuous linear (or not) map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups ℤ/nℤ, the integers ℤ, the torus 𝕋 and the real line. We also ask a related question for the twisted convolution.
George Gasper, Walter Trebels (1979)
Studia Mathematica
Al-Salam, Waleed A. (1995)
International Journal of Mathematics and Mathematical Sciences
Javad Namazi (1993)
Colloquium Mathematicae
Willi Freeden, Richard Reuter (1981)
Manuscripta mathematica
Gavin Brown, David C. Wilson (1989)
Mathematische Annalen
Edwin Hewitt, Gavin Brown (1984)
Mathematische Annalen
Góźdź, Stanisław (1999)
Balkan Journal of Geometry and its Applications (BJGA)
Michael Christ (1985)
Revista Matemática Iberoamericana
Daniel M. Oberlin (1982)
Colloquium Mathematicae
Daniel M. Oberlin (2003)
Colloquium Mathematicae
For 1 ≤ p,q ≤ ∞, we prove that the convolution operator generated by the Cantor-Lebesgue measure on the circle is a contraction whenever it is bounded from to . We also give a condition on p which is necessary if this operator maps into L²().
W. Connett, A. Schwartz (1975)
Studia Mathematica
H. Shapiro (1979)
Banach Center Publications
J. Bourgain, H. Sato (1986)
Studia Mathematica
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