On the absolute convergence factors of an orthogonal series
On the absolute summability of series with respect to block-orthonormal systems.
On the a.e. Divergence of the arithmetic means of double orthogonal series
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 constant in Meńshov-Rademacher inequality.
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 eigenstructure of the Bernstein kernel.
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...
On the Hartogs-type series for harmonic functions on Hartogs domains in , m ≥ 2
We study series expansions for harmonic functions analogous to Hartogs series for holomorphic functions. We apply them to study conjugate harmonic functions and the space of square integrable harmonic functions.
On the Hermite expansions of functions from the Hardy class
Considering functions f on ℝⁿ for which both f and f̂ are bounded by the Gaussian , 0 < a < 1, we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for O(n)-finite functions, thus extending a one-dimensional result of Vemuri.
On the Multiresolution analysis of abstract Hilbert spaces
On the Pseudodilation Representations of Flornes, Grossman, Holschneider, and Torresani.
On the rearranged block-orthonormal systems.
On the representation systems with respect to summation methods
Properties of representation systems with respect to summation methods are studied. For a given representation system with respect to a given summation method we study, in particular, the question of the stability of that property after deleting finitely many elements. As a consequence we obtain the existence of null series for the systems with respect to a given method of summation.
On the Reproducing Formula of Calderon.
On the Riesz summability of orthogonal series
On the Riesz-Fischer theorem for vector-valued functions
Open problems in constructive function theory.