Related papers: Extension of Bernstein Polynomials to Infinite Dim…
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…
A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…
I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
In this work, we introduce new approximation operators for univariate set-valued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new…
We consider stochastic differential equations in a Hilbert space, perturbed by the gradient of a convex potential. We investigate the problem of convergence of a sequence of such processes. We propose applications of this method to…
Bernstein polynomial approximation to a continuous function has a slower rate of convergence as compared to other approximation methods. "The fact seems to have precluded any numerical application of Bernstein polynomials from having been…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
The classical $L^2$ estimate for the $\overline{\partial}$ operators is a basic tool in complex analysis of several variables. Naturally, it is expected to extend this estimate to infinite dimensional complex analysis, but this is a…
We formulate a multi-valued version of the Tietze-Urysohn extension theorem. Precisely, we prove that any upper semicontinuous multi-valued map with nonempty closed convex values defined on a closed subset (resp. closed perfectly normal…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
This paper is concerned with a certain aspect of the spectral theory of unitary operators in a Hilbert space and its aim is to give an explicit construction of continuous functions of unitary operators. Starting from a given unitary…
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
The Fourier extension method, also known as the Fourier continuation method, is a method for approximating non-periodic functions on an interval using truncated Fourier series with period larger than the interval on which the function is…
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.
Kinematic algebras can be realised on geometric spaces and constrain the physical models that can live on these spaces. Different types of kinematic algebras exist and we consider the interplay of these algebras for non-relativistic limits…
We prove that several forms of the Bernstein polynomials with integer coefficients possess the property of simultaneous approximation, that is, they approximate not only the function but also its derivatives. We establish direct estimates…