A characterization of algebraic measures
A characterization of Fourier transforms
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.
A characterization of the minimal strongly character invariant Segal algebra
For a locally compact, abelian group , we study the space of functions on belonging locally to the Fourier algebra and with -behavior at infinity. We give an abstract characterization of the family of spaces abelian by its hereditary properties.
A Compactness Property of Fourier-Stieltjes Transforms
A Freĭman-type theorem for locally compact abelian groups
Suppose that is a locally compact abelian group with a Haar measure . The -ball of a continuous translation invariant pseudo-metric is called -dimensional if for all . We show that if is a compact symmetric neighborhood of the identity with for all , then is contained in an -dimensional ball, , of positive radius in some continuous translation invariant pseudo-metric and .
A geometrical property of causal invertible systems.
A multiplier theorem for continuous measures
A note on translates of bounded measures
A property of Fourier Stieltjes transforms on the discrete group of real numbers
Let be a Fourier-Stieltjes transform, defined on the discrete real line and such that the corresponding measure on the dual group vanishes on the set of characters, continuous on . Then for every , has a vanishing interior Lebesgue measure. If the statement is not generally true. The result is applied to prove a theorem of Rosenthal.
A remark on entropy of Abelian groups and the invariant uniform approximation property
A remark on Fourier-Stieltjes transform
A theorem concerning the multipliers for functions with Fourier transforms in
A Uniform Boundedness Principle for Compact Sets and the Decay of Fourier Transforms.
Abschätzung von Normen gewisser Matrizen und eine Anwendung.
Absolute convergence of Fourier series on finite-dimensional groups
Adèles et séries trigonométriques spéciales
An elementary proof of the decomposition of measures on the circle group
We give an elementary proof for the case of the circle group of the theorem of O. Hatori and E. Sato, which states that every measure on a compact abelian group G can be decomposed into a sum of two measures with a natural spectrum and a discrete measure.
An extension of a theorem of F. Forelli.
An Order Theoretical Characterization of the Fourier Transform.
Analytic measure and quasi-invariant measure