Related papers: Global approximation theorems for general gamma ty…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
Ideas and results of the generalized wave operator theory for dynamical and stationary cases are developed further and exact expressions for generalized scattering operators are obtained for wide classes of differential equations. New…
By using commutator methods, we show uniform resolvent estimates and obtain globally smooth operators for self-adjoint injective homogeneous operators $H$ on graded groups, including Rockland operators, sublaplacians and many others. Left…
Formulas for Galerkin-Koornwinder (GK) approximations of delay differential equations are summarized. The functional analysis ingredients (semigroups, operators, etc.) are intentionally omitted to focus instead on the formulas required to…
Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate the adjoint to that Hausdorff operator of the given function. We find the formulas for the rate of approximation in various metrics in…
This paper considers universal Hilbert space operators in the sense of Rota, and gives criteria for universality of semigroups in the context of uniformly continuous semigroups and contraction semigroups. Specific examples are given.…
The global homeomorphism theorem for quasiconformal maps describes the following specifically higher-dimensional phenomenon: {\em Locally invertible quasiconformal mapping $f: {\R}^{n} \to {\R}^{n}$ is globally invertible provided $n > 2$.}…
In this paper, we find new integral representations for the generalized Hermite linear functional in the real line and the complex plane. As an application, new integral representations for the Euler Gamma function are given.
his paper deals with approximating properties of the newly defined $q$-generalization of the Sz\'{a}sz operators in the case $q>1$. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem…
This paper proposes a specific type of Local Linear Model, the Shuffled Linear Model (SLM), that can be used as a universal approximator. Local operating points are chosen randomly and linear models are used to approximate a function or…
We establish $L^p$-type universal approximation theorems for general and non-anticipative functionals on suitable rough path spaces, showing that linear functionals acting on signatures of time-extended rough paths are dense with respect to…
In this work we provide a criterion for the global weak (1,1) type of integral operators which are known to be locally uniformly of weak (1,1) type. As an application, we establish the global weak (1,1) type for a class of Fourier integral…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…
The article $-$ part of a larger thesis which aims to give a detailed description of the generalisation to the category of groups with operators of the classical theory of semisimplicity for modules $-$ presents a straightforward…
We consider weighted uniform convergence of entire analogues of the Gr\"unwald operator on the real line. The main result deals with convergence of entire interpolations of exponential type $\tau>0$ at zeros of Bessel functions in spaces…
We expose the most advanced equiconvergence results for Birkhoff- and Stone-regular differential operators and present also author's approach to this problem. We give a full proof of equiconvergence on the whole interval, which constitutes…
We show that for integral operators of general form the norm bounds in Lorentz spaces imply certain norm bounds for the maximal function. As a consequence, the a.e. convergence for the integral operators on the Lorentz spaces follows from…
In \cite{5} we proved that generically functions defined in any open set can be approximated by a sequense of their pad\'{e} approximants, in the sense of uniform convergence on compacta. In this paper we examine a more particular space,…
Approximation theory is a substantial field of mathematical analysis that emerged in the 19th century and has been developed by mathematicians across the globe ever since. Its importance has increased over time, as it provides solutions to…