Related papers: Hermite-Pad\'e approximation for certain systems o…
In this paper we introduce vector-valued Hermite expansions to approximate one-parameter operator families such as $C_0$-groups and cosine functions. In both cases we estimate the rate of convergence of these Hermite expansions to the…
In \cite{5} we proved that generically functions defined in any open set can be approximated by a sequense of their pad\'{e} approximants, in the sense of uniform convergence on compacta. In this paper we examine a more particular space,…
We introduce meshfree finite difference methods for approximating nonlinear elliptic operators that depend on second directional derivatives or the eigenvalues of the Hessian. Approximations are defined on unstructured point clouds, which…
We establish Hermite expansion characterizations for several subspaces of the Fr\'{e}chet space of functions on the real line satisfying \begin{equation*} |f(x)| \lesssim e^{-(\frac{1}{2} - \lambda ) x^{2}} , \qquad | \widehat{f}(\xi )|…
We point out that resonance saturation in QCD can be understood in the large-Nc limit from the mathematical theory of Pade Approximants to meromorphic functions. These approximants are rational functions which encompass any saturation with…
In this paper, we analyze the convergence behavior of Hermite-type sampling Kantorovich operators in the context of mixed norm spaces. We prove certain direct approximation theorems, including the uniform convergence theorem, the…
The objective of this paper is to investigate the existence and the forms of the pair of finite order entire and meromorphic solutions of some certain systems of Fermat-type partial differential-difference equations of several complex…
We investigate generalized Laurent multiple orthogonal polynomials on the unit circle satisfying simultaneous orthogonality conditions with respect to $r$ probability measures or linear functionals on the unit circle. We show that these…
The Hermite-Taylor method evolves all the variables and their derivatives through order $m$ in time to achieve a $2m+1$ order rate of convergence. The data required at each node of the staggered Cartesian meshes used by this method makes…
In this paper we derive approximate quasi-interpolants when the values of a function $u$ and of some of its derivatives are prescribed at the points of a uniform grid. As a byproduct of these formulas we obtain very simple approximants…
Recent work has shown that parameterizing and optimizing coordinate transformations using normalizing flows, i.e., invertible neural networks, can significantly accelerate the convergence of spectral approximations. We present the first…
We study the convergence of the Hermite series of measurable functions on the real line. We characterize the norm convergence of truncated partial Hermite sums in rearrangement invariant spaces provided that the truncations vanish…
Type I Hermite--Pad\'e polynomials for a set of functions $f_0, f_1, ..., f_s$ at infinity, $Q_{n,0}$, $Q_{n,1}$, ..., $Q_{n,s}$, is defined by the asymptotic condition $$…
We establish a relation between the approximation in $L^2[-\pi,\pi]$ by exponentials with the set of frequencies of Beurling--Malliavin density less than $1$ and the meromorphic interpolation at $\mathbb Z$. Furthermore, we show that…
An algebraic function of the third order plays an important role in the problem of asymptotics of Hermite-Pad\'e approximants for two analytic functions with branch points. This algebraic function appears as the Cauchy transform of the…
In this paper we obtained some direct and inverse theorems of approximation theory for $\psi$-differentiable functions in the metric weighted Orlicz spaces with weights, which belong to the class of Muckenhoupt.
The main purpose of this paper is to determine the approximations of Durrmeyer modification of Szasz-Mirakjan operators, defined by Mishra et al. (Boll. Unione Mat. Ital. (2016) 8(4):297-305). We estimate the order of approximation of the…
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
By making a seminal use of the maximum modulus principle of holomorphic functions we prove existence of $n$-best kernel approximation for a wide class of reproducing kernel Hilbert spaces of holomorphic functions in the unit disc, and for…
In this article, we construct operator models for meromorphic functions of bounded type on Krein spaces. This construction is based on certain reproducing kernel Hilbert spaces which are closely related to model spaces. Specifically, we…