By using the technique of factoring weakly compact operators through reflexive Banach spaces we prove that a class of ordinary differential equations with Lipschitz continuous perturbations has a strong solution when the problem is governed by a closed linear operator generating a strongly continuous semigroup of compact operators.

Let T be a singular nonintegral operator; that is, it does not have an integral representation by a kernel with size estimates, even rough. In this paper, we consider the boundedness of commutators with T and Lipschitz functions. Applications include spectral multipliers of self-adjoint, positive operators, Riesz transforms of second-order divergence form operators, and fractional power of elli...

The aim of this paper is to show that under some mild conditions a functional equation of multiplicative $(alpha,beta)$-derivation is superstable on standard operator algebras. Furthermore, we prove that this generalized derivation can be a continuous and an inner $(alpha,beta)$-derivation.

In this paper, we introduce the concept of \(\mathbb{B}_{\alpha}\)-classical orthogonal polynomials, where \(\mathbb{B}_{\alpha}\) is raising operator \(\mathbb{B}_{\alpha}:=x^2 \cdot {d}/{dx}+\big(2(\alpha-1)x+1\big)\mathbb{I}\), with nonzero complex number \(\alpha\) and \(\mathbb{I}\) representing identity operator. We show that Bessel polynomials \(B^{(\alpha)}_n(x),\ n\geq0\), \(\alpha\neq...

in this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in f(t,x(t))dt +g(t,x(t))dw_t$ in which the multifunction $f$ is semimonotone and hemicontinuous and the operator-valued multifunction $g$ satisfies a lipschitz condition. we define the it^{o} stochastic integral of operator set-valued stochastic pr...

We study the problem of reconstructing solutions inverse problems when only noisy measurements are available. assume that can be modeled with an infinite-dimensional forward operator is not continuously invertible. Then, we restrict this to finite-dimensional spaces so Lipschitz continuous. For operator, demonstrate there exists a neural network which robust-to-noise approximation operator. In ...

Abstract The main purpose of this article is to establish some new characterizations the (variable) Lipschitz spaces in terms boundedness commutator multilinear fractional Calderón-Zygmund integral operators context variable exponent Lebesgue spaces. authors do so by applying techniques Fourier series and operator, as well pointwise estimates for commutators. key tool obtaining such a estimate ...

In this paper, we study the differentiation operator acting on discrete function spaces; that is spaces of functions defined an infinite rooted tree. We discuss, through its connection with composition operators, boundedness and compactness operator. addition, discuss norm spectrum, consider when such can be isometry. then apply these results to Lipschitz space weighted Banach spaces, as well H...

We prove a new criterion that guarantees self-adjointness of Toeplitz operators with unbounded operator-valued symbols. Our applies, in particular, to symbols Lipschitz continuous derivatives, which is the natural class Hamiltonian functions for classical mechanics. For this we extend Berger-Coburn estimate case vector-valued Segal-Bargmann spaces. Finally, apply our result (operator-valued) qu...