Related papers: Taylor approximations of operator functions
This note deals with the boundedness of the $H^\infty$ functional calculus of Ritt operators $T$ and associated square function estimates. The purpose is to give a shorter, concise and slightly more general approach towards Le~Merdy's…
This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.
Operator $k$-tone functions on an open interval of the real line, which are higher order extensions of operator monotone and convex functions, are characterized via certain inequalities for the real and imaginary parts of analytic…
The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.
In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates Korovkin and direct approximation results using second…
The new notion of operator/matrix $k$-tone functions is introduced, which is a higher order extension of operator/matrix monotone and convex functions. Differential properties of matrix $k$-tone functions are shown. Characterizations,…
Construction of analytic functions, which determine bounded Toeplitz operators
We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the…
In this paper, we present an approach to enhance interpolation and approximation error estimates. Based on a previously derived first-order Taylor-like formula, we demonstrate its applicability in improving the $P_1$-interpolation error…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
The aim of this paper is to establish various factorization results and then to derive estimates for linear functionals through the use of a generalized Taylor theorem. Additionally, several error bounds are established including…
We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.
We consider the problem of under and over-approximating the image of general vector-valued functions over bounded sets, and apply the proposed solution to the estimation of reachable sets of uncertain non-linear discrete-time dynamical…
Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
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…
In this paper, we will show a new characterization of operator monotone functions by a matrix reverse Cauchy inequality.
We analyze the Lipkin Model using effective operator techniques. We present both analytical and numerical results for effective Hamiltonians. The accuracy of the cluster approximation is investigated.
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…