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We study volumes of sections of convex origin-symmetric bodies in $\mathbb{R}% ^{n}$ induced by orthonormal systems on probability spaces. The approach is based on volume estimates of \ John-L\"{o}wner ellipsoids and expectations of norms…
In this paper we consider a generalized conditional-type Holder- inequality and investigate some classic properties of multiplication conditional expectation type operators on Orlicz-spaces.
Approximation properties of multivariate quasi-projection operators are studied in the paper. Wide classes of such operators are considered, including the sampling and the Kantorovich-Kotelnikov type operators generated by different…
We study the best approximation and distance problems in the operator space $\B(\HS)$ and in the space of trace class operators $\LS^1(\B(\HS))$. Formulations of distances are obtained in both cases. The case of finite-dimensional…
In this work, we develop a unified framework for quasidiagonal and F\o lner-type approximations of linear operators on Hilbert spaces. These approximations (originally formulated for bounded operators and operator algebras) involve…
The boundedness (continuity) of composition operators from some function space to another one is significant, though there are few results about this problem. Thus, in this study, we provide necessary and sufficient conditions on the…
We show that the Schr\"odinger operator associated with a physical system over a local field can be approximated in a very strong sense by finite Schr\"odinger operators. Some striking numerical results are included at the end of the…
Operator learning based on neural operators has emerged as a promising paradigm for the data-driven approximation of operators, mapping between infinite-dimensional Banach spaces. Despite significant empirical progress, our theoretical…
We give embedding theorems for weighted Bergman-Orlicz spaces on the ball and then apply our results to the study of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted…
We study two types of approximations of Lipschitz maps with derivatives of maximal slopes on Banach spaces. First, we characterize the Radon-Nikod\'ym property in terms of strongly norm attaining Lipschitz maps and maximal derivative…
We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data…
We develop a general, functional calculus approach to approximation of $C_0$-semigroups on Banach spaces by bounded completely monotone functions of their generators. The approach comprises most of well-known approximation formulas, yields…
We study approximation of functions by algebraic polynomials in the H\"older spaces corresponding to the generalized Jacobi translation and the Ditzian-Totik moduli of smoothness. By using modifications of the classical moduli of…
We study best approximations in Banach spaces via Birkhoff-James orthogonality of functionals. To exhibit the usefulness of Birkhoff-James orthogonality techniques in the study of best approximation problems, some algorithms and distance…
We study mapping properties of two-dimensional linear integral operators in some weighted spaces with special kernels. The considered spaces are certain variant of Sobolev--Slobodetskii spaces and their generalizations related to Banach…
The set of badly approximable $m \times n $ matrices is known to have Hausdorff dimension $mn $. Each such matrix comes with its own approximation constant $c$, and one can ask for the dimension of the set of badly approximable matrices…
This paper explores the concept of approximate Birkhoff-James orthogonality in the context of operators on semi-Hilbert spaces. These spaces are generated by positive semi-definite sesquilinear forms. We delve into the fundamental…
In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others…
In this paper, convergence results in a multivariate setting have been proved for a family of neural network operators of the max-product type. In particular, the coefficients expressed by Kantorovich type means allow to treat the theory in…
Characterizations are given for 1-complemented hyperplanes of strictly monotone real Lorentz spaces and 1-complemented finite codimensional subspaces (which contain at least one basis element) of real Orlicz spaces equipped with either…