Faltungsungleichungen auf endlichen abelschen Gruppen.
Fermés d'unicité dans les groupes abéliens localement compacts
Fractal multiwavelets related to the Cantor dyadic group.
Generalization of the theorem on the argument of almost periodic function
Generalized functions on adeles. Linear and non-linear theories
We consider various generalizations of linear homogeneous distributions on adeles and construct a number of algebras of non-linear generalized functions on adeles and totally disconnected groups such as the discrete adeles.
Group Representations which Vanish at Infinity.
Haar system on a product of zero-dimensional compact groups
In this work, we study the problem of constructing Haar bases on a product of arbitrary compact zero-dimensional Abelian groups. A general scheme for the construction of Haar functions is given for arbitrary dimension. For dimension d=2, we describe all Haar functions.
Haar wavelets on the Lebesgue spaces of local fields of positive characteristic
We construct the Haar wavelets on a local field K of positive characteristic and show that the Haar wavelet system forms an unconditional basis for , 1 < p < ∞. We also prove that this system, normalized in , is a democratic basis of . This also proves that the Haar system is a greedy basis of for 1 < p < ∞.
Harmonic Analysis and Real Group Algebras.
Harmonic analysis of Abelian inner automorphism groups of von Neumann algebras.
Herz-type Besov spaces on locally compact Vilenkin groups.
Homogeneous Besov spaces on locally compact Vilenkin groups
Independence with respect to families of characters
Interpolation by the Fourier-Stieltjes transform of a positive compactly supported measure
Linear combinations of generators in multiplicatively invariant spaces
Multiplicatively invariant (MI) spaces are closed subspaces of L²(Ω, ) that are invariant under multiplication by (some) functions in ; they were first introduced by Bownik and Ross (2014). In this paper we work with MI spaces that are finitely generated. We prove that almost every set of functions constructed by taking linear combinations of the generators of a finitely generated MI space is a new set of generators for the same space, and we give necessary and sufficient conditions on the linear...
Majoration de la transformée de Fourier de certaines mesures
Soit une fonction polynôme de dans . On considère la mesure sur le graphe de dont la projection sur est la mesure de Lebesgue. On étudie ici le comportement de la transformée de Fourier lorsque approche de 0 (de telles distributions apparaissent comme caractères de représentations de groupes de Lie nilpotents). On étend des résultats de L. Corwin et F.P. Greenleaf (Comm. on Pure and Applied Math., 31 (1975), 681–705) au cas où le gradient de la partie de homogène de plus haut degré...
Mean periodic functions on phase space and the Pompeiu problem with a twist
We show that when is a mean periodic function of tempered growth on the reduced Heisenberg group then the closed translation and rotation invariant subspace generated by contains an elementary spherical function. Using a Paley-Wiener theorem for the Fourier-Weyl transform we formulate a conjecture for arbitrary mean periodic functions.
Measure characteristics of complexes
Measures and Convolution Products with Small Transforms.
Multipliers on subsemigroups of locally compact abelian groups.