expansions in series of fractional parts.
boundedness of Riesz transforms for orthogonal polynomials in a general context
Nowak and Stempak (2006) proposed a unified approach to the theory of Riesz transforms and conjugacy in the setting of multi-dimensional orthogonal expansions, and proved their boundedness on L². Following them, we give easy to check sufficient conditions for their boundedness on , 1 < p < ∞. We also discuss the symmetrized version of these transforms.
norm convergence of rational operators on the unit circle.
Lattice Size Estimates for Gabor Decompositions.
L'espace usuel C ne possede aucun R.U.C-systeme orthonorme.
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...
Localization and Convergence of Eigenfunction Expansions.