相关论文: Approximation properties of Bernstein singular int…
The class of location-scale finite mixtures is of enduring interest both from applied and theoretical perspectives of probability and statistics. We prove the following results: to an arbitrary degree of accuracy, (a) location-scale…
In this paper, we investigate the geometric properties of the variable mixed Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We show that, if $ 1<q_-,p_-,q_+,p_+<\infty $, then $\ell^{q(\cdot)} (L^{p(\cdot)})$ is…
Disjointly strictly singular inclusions between variable Lebesgue spaces $L^{p(\cdot)}(\mu)$ on finite measure are characterized. Suitable criteria in terms of the (bounded or unbounded) exponents are given. It is proved the equivalence of…
In this paper, we extend several approximation theorems, originally formulated in the context of the standard $L^p$ norm, to the more general framework of variable exponent spaces. Our study is motivated by applications in neural networks,…
This review paper highlights the main aspects of the development of research related to the solution of extreme problems in the theory of approximation in the spaces ${\mathcal S}^p$ and $B{\mathcal S}^p$ of periodic and almost periodic…
We consider the space of functions almost in $L_p$ and endow it with the topology of asymptotic $L_p$-convergence. This yields a completely metrizable topological vector space which, on finite measure spaces, coincides with the space of…
We introduce another new type of combinations of Bernstein operators in this paper, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type…
In this paper we prove the bounded approximation property for variable exponent Lebesgue spaces, study the concept of nuclearity on such spaces and apply it to trace formulae such as the Grothendieck-Lidskii formula. We apply the obtained…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
Many elliptic boundary value problems exhibit an interior regularity property, which can be exploited to construct local approximation spaces that converge exponentially within function spaces satisfying this property. These spaces can be…
We show that on separable Banach spaces admitting a separating polynomial, any uniformly continuous, bounded, real-valued function can be uniformly approximated by Lipschitz, analytic maps on bounded sets.
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
We give conditions on the exponent function $p(\cdot)$ that imply the existence of embeddings between grand, small and variable Lebesgue spaces. We construct examples to show that our results are close to optimal. Our work extends recent…
This article explores the extension of the classical approximation property and its variants to the nonlinear framework of Lipschitz operator theory. Building on Grothendieck's tensor product methodology, we characterize the Lipschitz…
We consider Gaussian Besov spaces obtained by real interpolation and Riemann-Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension.…
In this paper we establish asymptotically best possible interpolation Lebesgue-type inequalities for $2\pi$-periodic functions $f$, which are representable as generalized Poisson integrals of the functions $\varphi$ from the space $L_p$,…
In a previous paper, we introduced a new class of Gaussian singular integrals, that we called the general alternative Gaussian singular integrals and study the boundedness of them on $L^p(\gamma_d)$, $ 1 < p < \infty.$ In this paper, we…
Direct and inverse approximation theorems are proved in the Besicovitch-Stepanets spaces $B{\mathcal S}^{p}$ of almost periodic functions in terms of the best approximations of functions and their generalized moduli of smoothness.
We establish inverse and direct theorems on best approximations in quasi-normed Abelian groups through bilateral Bernstein-Jackson inequalities with exact constants. Using integral representations for quasi-norms of functions $f$ in…
We analyze Bergman spaces A p f (D) of generalized analytic functions of solutions to the Vekua equation $\partial$w = ($\partial$f /f)w in the unit disc of the complex plane, for Lipschitz-smooth non-vanishing real valued functions f and 1…