For real functions of bounded variation in the Hardy sense, -periodic in each variable, the rates of pointwise convergence of the Borel and Euler means of their Fourier series are estimated.
Considering the class of almost periodic functions integrable in the Stepanov sense we extend and generalize certain results of the first author, as well as of L. Leindler and P. Chandra.
We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value problems,...
Using classical results on conjugate functions, we give very short proofs of theorems of Erdös–Turán and Blatt concerning the angular distribution of the roots of polynomials. Then we study some examples.
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...
Necessary and sufficient conditions for the existence of compactly supported -solutions for the two-dimensional two-scale dilation equations are given.
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.