On the Asymptotic Behaviour of the Gthetak-means of Eigenfunction Expansion Related to the Slowly Oscillating Functions With Remainder Term
On the best constants in the Khinchin inequality
On the boundary convergence of solutions to the Hermite-Schrödinger equation
In the half-space , consider the Hermite-Schrödinger equation i∂u/∂t = -Δu + |x|²u, with given boundary values on . We prove a formula that links the solution of this problem to that of the classical Schrödinger equation. It shows that mixed norm estimates for the Hermite-Schrödinger equation can be obtained immediately from those known in the classical case. In one space dimension, we deduce sharp pointwise convergence results at the boundary by means of this link.
On the bundle convergence of double orthogonal series in noncommutative -spaces
The notion of bundle convergence in von Neumann algebras and their -spaces for single (ordinary) sequences was introduced by Hensz, Jajte, and Paszkiewicz in 1996. Bundle convergence is stronger than almost sure convergence in von Neumann algebras. Our main result is the extension of the two-parameter Rademacher-Men’shov theorem from the classical commutative case to the noncommutative case. To our best knowledge, this is the first attempt to adopt the notion of bundle convergence to multiple series....
On the computation of scaling coefficients of Daubechies' wavelets
In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.
On the conjecture of Gát.
On the constant in Meńshov-Rademacher inequality.
On the convergence and summability of -dimensional Fourier series with respect to the Walsh-Paley systems in the spaces , .
On the convergence and summability of series with respect to block-orthonormal systems.
On the (C,α≥0,β≥0)-summability of double orthogonal series
On the decay properties of the Franklin analyzing wavelet
On the denseness of Jacobi polynomials.
On the direct kernels with respect to the Walsh-Kaczmarz system.
On the discrete wavelet transform of stochastic processes.
On the distributional orthogonality of the general Pollaczek polynomials.
On the eigenstructure of the Bernstein kernel.
On the exact values of coefficients of coiflets
In 1989, R. Coifman suggested the design of orthonormal wavelet systems with vanishing moments for both scaling and wavelet functions. They were first constructed by I. Daubechies [15, 16], and she named them coiflets. In this paper, we propose a system of necessary conditions which is redundant free and simpler than the known system due to the elimination of some quadratic conditions, thus the construction of coiflets is simplified and enables us to find the exact values of the scaling coefficients...
On the existence of a compactly supported -solution for two-dimensional two-scale dilation equations
Necessary and sufficient conditions for the existence of compactly supported -solutions for the two-dimensional two-scale dilation equations are given.
On the existence of non-linear frames
A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if is a Banach space such that has a SRBF, then has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space has an approximative Schauder frame, then has a SRBF. Finally, the existence of a non-linear SRBF in the conjugate of a separable Banach space has been proved.
On the existence of wavelets for non-expansive dilation matrices.
Sets which simultaneously tile Rn by applying powers of an invertible matrix and translations by a lattice are studied. Diagonal matrices A for which there exist sets that tile by powers of A and by integer translations are characterized. A sufficient condition and a necessary condition on the dilations and translations for the existence of such sets are also given. These conditions depend in an essential way on the interplay between the eigenvectors of the dilation matrix and the translation lattice...