相关论文: Uniform convergence of translation operators

Motivated by the rapidly growing field of mathematics for operator approximation with neural networks, we present a novel universal operator approximation theorem for a broad class of encoder-decoder architectures. In this study, we focus…

In this work we obtain the pointwise almost everywhere convergence for two families of multilinear operators: (a) truncated homogeneous singular integral operators associated with $L^q$ functions on the sphere and (b) lacunary multiplier…

An example due to Pisier shows that two commuting, completely polynomially bounded Hilbert space operators may not be simultaneously similar to contractions. Thus, while each operator is individually similar to a contraction, the pair is…

The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…

In the present paper, an inverse result of approximation, i.e., a saturation theorem for the sampling Kantorovich operators is derived, in the case of uniform approximation for uniformly continuous and bounded functions on the whole real…

This note concerns uniform equicontinuity of families of operators on a separable Hilbert space H, and of families of maps on B(H). It is shown that a one parameter group of automorphisms is uniformly equicontinuous if and only if the group…

Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…

We study translation preserving operators, that is operators commuting with translations by a closed subgroup of a locally compact abelian group. We show that there is a one to one correspondence between these operators and range operators.…

In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.

We introduce a notion of uniformly continuous orbit equivalence as a subequivalence relation of continuous orbit equivalence of one-sided topological Markov shifts. It is described in terms of gauge actions on the associated Cuntz-Krieger…

The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations.…

In this paper we give a unitary approach for the simultaneous study of the convergence of discrete and integral operators described by means of a family of linear continuous functionals acting on functions defined on locally compact…

We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.

We will investigate the norm closure of the unitary and similarity orbits of normal operators in unital, simple, purely infinite C*-algebras. An operator theoretic proof will be given to the classification of when two normal operators are…

In this paper, we construct generalized Baskakov Kantorovich operators. We establish some direct results and then study weighted approximation, simultaneous approximation and statistical convergence properties for these operators. Finally,…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

It is well known that the Riemann zeta function, as well as several other $L$-functions, is universal in the strip $1/2<\sigma<1$; this is certainly not true for $\sigma>1$. Answering a question of Bombieri and Ghosh, we give a simple…

The goal of universal machine translation is to learn to translate between any pair of languages, given a corpus of paired translated documents for \emph{a small subset} of all pairs of languages. Despite impressive empirical results and an…

The present paper deals with construction of newly family of Neural Network operators, that is, Steklov Neural Network operators. By using Steklov type integral, we introduce a new version of Neural Network operators and we obtain some…