Related papers: Beyond Dominated Convergence: Newer Methods of Int…
A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play main role instead of thin or finite sets which removes some…
A new approach to disintegration of measures is presented, allowing one to drop the usually taken separability assumption. The main tool is a result on fibers in the spectrum of algebra of essentially bounded functions established recently…
The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions…
Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…
Given a compact metric space $X$ and a probability measure in the $\sigma-$algebra of Borel subsets of $X$, we will establish a dominated convergence theorem for ultralimits of sequences of integrable maps and apply it to deduce a…
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper. The results are given in terms of $L^p$ integrability of the function and its…
Discrete analogs of the Lebedev transforms with the product of the modified Bessel functions are introduced and investigated. Several expansions of suitable functions and sequences in terms of the series and integrals, involving the…
The purpose of this article is to develop an algebraic approach to the problem of integrable classification of differential-difference equations with one continuous and two discrete variables. As a classification criterion, we put forward…
In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type…
A criterion for determining exactly when an order of a maximal subfield of a central simple algebra over a number field can be embedded into an order of this algebra is given. Various previous results have been generalized and recovered by…
We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce…
An integral on Euclidean space, equivalent to the Lebesgue integral, is constructed by extending the notion of Riemann sums. In contrast to the Henstock--Kurzweil and McShane integrals, the construction recovers the full measure-theoretic…
Considering the sets of subsums of series (or achievement sets) we show that for conditionally convergent series the multidimensional case is much more complicated than that of the real line. Although we are far from the full topological…
Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…
This paper proposes a new theory and methodology to tackle the problem of unifying distributed analyses and inferences on shared parameters from multiple sources, into a single coherent inference. This surprisingly challenging problem…
We study the convergence analysis of continuous-time dynamical systems associated with optimization methods for strongly convex functions. Recent works have proposed systematic constructions of Lyapunov functions for such analysis, while…
A family of general Master theorems for analytic integration over the real (or imaginary) axis with various reciprocal hyperbolic (trig) kernels ($\sinh and/or \cosh$) with varying arguments is developed. Several examples involving…
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \geq 3$ dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model…
A necessary and sufficient condition is provided for the solvability of a binomial congruence with a composite modulus, circumventing its prime factorization. This is a generalization of Euler's Criterion through that of Euler's Theorem,…
We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…