On convergence of Fourier series of functions of generalized bounded variation
On convergence of greedy approximations for the trigonometric system.
On convergence of orthogonal series of Bessel functions
On convergence of orthonormal expansions for exponential weights.
On convergence of the Fourier series of a constructive function of weakly bounded variation
On convergence subsystems of orthonormal systems.
On converse theorems of trigonometric approximation in weighted variable exponent Lebesgue spaces.
On convolution operators with small support which are far from being convolution by a bounded measure
Let be the left convolution operators on with support included in F and denote those which are norm limits of convolution by bounded measures in M(F). Conditions on F are given which insure that , and are as big as they can be, namely have as a quotient, where the ergodic space W contains, and at times is very big relative to . Other subspaces of are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.
On cosine polynomials corresponding to sets of integers
On counterexamples in multivariate approximation
On degrees of approximation of some classes by polynomials with respect to generalized Haar system.
On differentiation of integrals with respect to bases of convex sets.
Differentiation of integrals of functions from the class with respect to the basis of convex sets is established. An estimate of the rate of differentiation is given. It is also shown that there exist functions in , N ≥ 3, and with ω(δ)/δ → ∞ as δ → +0 whose integrals are not differentiated with respect to the bases of convex sets in the corresponding dimension.
On Discrete and Continous Norms in Paley-Wiener Spaces and Consequences for Exponential Frames.
On discrete Fourier spectrum of a harmonic with random frequency modulation
Asymptotic properties of the Discrete Fourier Transform spectrum of a complex monochromatic oscillation with frequency randomly distorted at the observation times t=0,1,..., n-1 by a series of independent and identically distributed fluctuations is investigated. It is proved that the second moments of the spectrum at the discrete Fourier frequencies converge uniformly to zero as n → ∞ for certain frequency fluctuation distributions. The observed effect occurs even for frequency fluctuations with...
On Discrete Frames Associated with Semidirect Products.
On Dualizing a Multivariable Poisson Summation Formula.
On embeddings, traces and multipliers in harmonic function spaces
On Entropy Bumps for Calderón-Zygmund Operators
We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ℇ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on Rd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound [...]
On Entropy Bumps for Calderón-Zygmund Operators
We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ɛ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on ℝd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound ||Tof||Lp(w) ≲ ||f|| Lp(o).
On equivalence question between the Ditzian-Totik modulus of smoothness and an usual periodic modulus of smoothness.