A note on comprehensive backward biorthogonalization.
A note on fusion Banach frames
For a fusion Banach frame for a Banach space , if is a fusion Banach frame for , then is called a fusion bi-Banach frame for . It is proved that if has an atomic decomposition, then also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a characterization of fusion bi-Banach frames is given.
A note on integer translates of a square integrable function on ℝ
We consider the subspace of L²(ℝ) spanned by the integer shifts of one function ψ, and formulate a condition on the family , which is equivalent to the weight function being > 0 a.e.
A note on semi-classical orthogonal polynomials.
A note on some expansions of p-adic functions
Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by . The system is defined in the space C(ℤₚ,ℂₚ) of ℂₚ-valued continuous functions on ℤₚ. J. Rutkowski has also considered some questions concerning expansions of functions from C(ℤₚ,ℂₚ) with respect to . This paper is a remark to Rutkowski’s paper. We define another system in C(ℤₚ,ℂₚ), investigate its properties and compare it to the system defined by Rutkowski. The system...
A note on the best approximation by ridge functions.
A note on the construction of nonseparable wavelet bases and multiwavelet matrix filters of , where .
A note on the magnitude of Walsh Fourier coefficients.
A note on the means
A note on wavelet bases in function spaces
A Note on Wavelets and S-asymptotics
A Paley type inequality for two-parameter Vilenkin-Fourier coefficients.
A proof of Pełczyński's conjecture for the Haar system
A remark on multiresolution analysis of
A condition on a scaling function which generates a multiresolution analysis of is given.
A remark on the multipliers of the Haar basis of L¹[0,1]
A proof of a necessary and sufficient condition for a sequence to be a multiplier of the normalized Haar basis of L¹[0,1] is given. This proof depends only on the most elementary properties of this system and is an alternative proof to that recently found by Semenov & Uksusov (2012). Additionally, representations are given, which use stochastic processes, of this multiplier norm and of related multiplier norms.
A restriction theorem for the Heisenberg motion
We prove a restriction theorem for the class-1 representations of the Heisenberg motion group. This is done using an improvement of the restriction theorem for the special Hermite projection operators proved in [13]. We also prove a restriction theorem for the Heisenberg group.
A set of orthogonal polynomials induced by a given orthogonal polynomial.
A sharp estimate of the measure of the set of divergence of multiple orthogonal Fourier series
The aim of this paper is to obtain sharp estimates from below of the measure of the set of divergence of the m-fold Fourier series with respect to uniformly bounded orthonormal systems for the so-called G-convergence and λ-restricted convergence. We continue the study begun in a previous work.
A Sharper Stability Bound of Fourier Frames.
A survey of certain results on strong approximation by orthogonal series
This is a survey of results in a particular direction of the theory of strong approximation by orthogonal series, related mostly with author's contributions to the subject.