Related papers: Multivariate fractal interpolation functions: Some…
Given a multi-valued function $\Phi$ on a topological space $X$ we study the properties of its fixed fractal, which is defined as the closure of the orbit $\Phi^\omega(Fix(\Phi))=\bigcup_{n\in\omega}\Phi^n(Fix(\Phi))$ of the set…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…
We develop the theory of fractal homeomorphisms generated from pairs of overlapping affine iterated function systems.
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…
Fractal Interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse-grained Navier-Stokes equations. It is based on synthetically generating a scale-invariant…
A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results…
Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…
In this paper, we study the weighted inequality for multilinear fractional maximal operators and fractional integrals. We give sharp weighted estimates for both operators.
Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical…
We introduce a duality for Affine Iterated Function Systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems yield fractals defined by iteration of contractive affine…
We estimate the bounds of box-counting dimension of hidden variable fractal interpolation functions (HVFIFs) and hidden variable bivariate fractal interpolation functions (HVBFIFs) with four function contractivity factors and present…
In this paper, we study errors on perturbation of function contractivity factors and box-counting dimension of hidden variable recurrent fractal interpolation function (HVRFIF). The HVRFIF is a hidden variable fractal interpolation function…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…
Interpolation of classes of differentiated functions given on a finite interval by trigonometric splines using the phantom node method is considered. This method consists in supplementing a given sequence of values of an approximate…
This article pertains to interpolation of Sobolev functions at shrinking lattices $h\mathbb{Z}^d$ from $L_p$ shift-invariant spaces associated with cardinal functions related to general multiquadrics,…
This paper deals with approximation of smooth convex functions $f$ on an interval by convex algebraic polynomials which interpolate $f$ at the endpoints of this interval. We call such estimates "interpolatory". One important corollary of…
The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those…
The paper deals with the problem of approximating the functions of several variables by branched continued fractions, in particular, multidimensional A- and J-fractions with independent variables. A generalization of Gragg's algorithm is…