Old Friends Revisited; the Multifunctional Nature of Some Classical Functions.
On a Fourier-Bessel series of special kind
On a gap series of Mark Kac
Mark Kac gave an example of a function f on the unit interval such that f cannot be written as f(t)=g(2t)-g(t) with an integrable function g, but the limiting variance of vanishes. It is proved that there is no measurable g such that f(t)=g(2t)-g(t). It is also proved that there is a non-measurable g which satisfies this equality.
On a non-self adjoint eigenfunction expansion.
On -summability of orthogonal series
In the paper, we prove two theorems on summability, , of orthogonal series. Several known and new results are also deduced as corollaries of the main results.
On a.e. convergence of expansion with respect to a bounded orthonormal system of polygonals
On almost everywhere and mean convergence of Hermite and Laguerre expansions
On (C,1) summability for Vilenkin-like systems
We give a common generalization of the Walsh system, Vilenkin system, the character system of the group of 2-adic (m-adic) integers, the product system of normalized coordinate functions for continuous irreducible unitary representations of the coordinate groups of noncommutative Vilenkin groups, the UDMD product systems (defined by F. Schipp) and some other systems. We prove that for integrable functions σₙf → f (n → ∞) a.e., where σₙf is the nth (C,1) mean of f. (For the character system of the...
On Calderón-Toeplitz Operators.
On convergence subsystems of orthonormal systems.
On Euler means and T-means of orthogonal series
On Fourier series in eigenfunctions of elliptic boundary value problems.
On Lower Bounds of Exponential Frames.
On Multiresolution Analysis of Multiplicity d.
On recurrence property of Riesz-Raikov sums.
On strong Euler summability of orthogonal series
On the -problem in Weyl-Heisenberg frames
Let . We investigate the characterization problem which asks for a classification of all the triples such that the Weyl-Heisenberg system is a frame for . It turns out that the answer to the problem is quite complicated, see Gu and Han (2008) and Janssen (2003). Using a dilation technique, one can reduce the problem to the case where and only let and vary. In this paper, we extend the Zak transform technique and use the Fourier analysis technique to study the problem for the case of...
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