Related papers: Further analysis of Multivariate fractal functions
We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the O-sequences and encode some information on lex segment ideals. Moreover, we introduce a numerical functions…
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…
Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We characterize the region of meromorphic continuation of an analytic function $f$ in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of $f$. The rational approximants have a…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
A novel method for constructing a nonlinear fractal histopolation function associated with a given histogram is introduced in this paper. In contrast to classical fractal interpolation methods, which produce continuous and interpolatory…
For fixed natural numbers $r$ and $s$, where $2\leq s \leq r$, we consider a representation of numbers from the interval $[0;\frac{r}{s-1}]$ obtained by encoding numbers by means of the alphabet $A=\{0,1,...,r\}$ via the expansion…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
Multivariate quasi-projection operators $Q_j(f,\varphi, \widetilde{\varphi})$, associated with a function $\varphi$ and a distribution/function $\widetilde{\varphi}$, are considered. The function $\varphi$ is supposed to satisfy the…
This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there…
This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.
In this paper, we first present a simple lemma which allows us to estimate the box dimension of graphs of given functions by the associated oscillation sums and oscillation vectors. Then we define vertical scaling matrices of generalized…
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…
Approximation properties of periodic quasi-projection operators with matrix dilations are studied. Such operators are generated by a sequence of functions $\varphi_j$ and a sequence of distributions/functions $\widetilde{\varphi}_j$. Error…
In this paper, based on the results from [On the localization of Hutchinson-Barnsley fractals, Chaos Solitons Fractals, 173 (2023), 113674], we generate coverings (consisting of finite families of rhombi) of the graph of fractal…
Approximation properties of quasi-projection operators $Q_j(f,\varphi, \widetilde{\varphi})$ are studied. Such an operator is associated with a function $\varphi$ satisfying the Strang-Fix conditions and a tempered distribution…
We define fractal interpolation on unbounded domains for a certain class of topological spaces and construct local fractal functions. In addition, we derive some properties of these local fractal functions, consider their tensor products,…
In the preceding articles we considered fractional integral transforms involving one real scalar variable, one real matrix variable and real scalar multivariable case. In the present paper we consider the multivariable case when the…
We introduce the notion of structural derivative on time scales. The new operator of differentiation unifies the concepts of fractal and fractional order derivative and is motivated by lack of classical differentiability of some…