相关论文: Discrete Linear Interpolatory Operators
We associate to an integral operator a discrete one which is conceptually simpler, and study the relations between them.
In the present article, we propose the new class positive linear operators, which discrete type depending on a real parameters. These operators are similar to Jain operators but its approximation properties are different then Jain…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear…
We consider interpolation inequalities for imbeddings of the $l^2$-sequence spaces over $d$-dimensional lattices into the $l^\infty_0$ spaces written as interpolation inequality between the $l^2$-norm of a sequence and its difference. A…
The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…
We define a class of discrete operators that, in particular, include the delta and nabla fractional operators.
We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension we present a…
We study the interpolation and extrapolation properties of strictly singular operators between different $L_p$ spaces. To this end, the structure of strictly singular non-compact operators between $L_p-L_q$ spaces is analyzed. Among other…
In this paper, a new class of \emph{Taylor-accelerated neural network interpolation operators} is introduced on quasi-uniform irregular grids. These operators improve existing neural network interpolation operators by incorporating Taylor…
The main aims of this article are to characterize a class of operators associated with the symmetrized polydisc that admit rational dilations on the minimal space and to show an interplay between rational dilation and distinguished…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations. In contrast to conventional interpolation operators, these new interpolation operators maintain the strict…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
Univariate spline discrete quasi-interpolants (abbr. dQIs) are approximation operators using B-spline expansions with coefficients which are linear combinations of discrete values of the function to be approximated. When working with…
We introduce interpolation operators with approximation and stability properties suited for parabolic problems in primal and mixed formulations. We derive localized error estimates for tensor product meshes (occurring in classical…
We study some natural operators acting on configurations of points and lines in the plane and remark that many interesting configurations are fixed points for these operators. We review ancient and recent results on line or point…