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The representations of dimension vector $\alpha$ of the quiver Q can be parametrised by a vector space $R(Q,\alpha)$ on which an algebraic group $\Gl(\alpha)$ acts so that the set of orbits is bijective with the set of isomorphism classes…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
A \emph{fractal} is an object exhibiting complexity at arbitrarily small scales. In order to study and characterise fractals, one is often interested in quantifying how they fill up space on small scales. This gives rise to various notions…
Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…
In contrast to the univariate case, interpolation with polynomials of a given maximal total degree is not always possible even if the number of interpolation points and the space dimension coincide. Due to that, numerous constructions for…
This paper discusses an abstract Kramer sampling theorem for functions within a reproducing kernel Hilbert space (RKHS) of vector valued holomorphic functions. Additionally, we extend the concept of quasi Lagrange-type interpolation for…
We construct a class of super-reflexive complementably minimal spaces, and study uniformly convex distortions of the norm on Hilbert space by using methods of complex interpolation.
We study a wide class of fractal interpolation functions in a single platform by considering the domains of these functions as general attractors. We obtain lower and upper bounds of the box dimension of these functions in a more general…
This paper presents a new approach of constructing $\alpha$-fractal interpolation functions (FIFs) using neural network operators, integrating concepts from approximation theory. Initially, we construct $\alpha$-fractals utilizing neural…
We consider piecewise linear interpolation from the perspective of kernel interpolation and quadrature. If the Sobolev space $W_2^1(0, 1)$ is equipped with a suitable inner product, its reproducing kernel is piecewise linear and gives rise…
In this paper, the notion of dimension preserving approximation for real-valued bivariate continuous functions, defined on a rectangular domain $\rectangle$, has been introduced and several results, similar to well-known results of…
There are many research papers dealing with fractal dimension of real-valued fractal functions in the recent literature. The main focus of the present paper is to study fractal dimension of complex-valued functions. This paper also…
The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…
The construction of fractal generalized zone plates (FraGZPs) from a set of periodic diffractive optical elements with circular symmetry is proposed. This allows us to increase the number of foci of a conventional fractal zone plate…
Starting with a regular symmetric Dirichlet form on a locally compact separable metric space $X$, our paper studies elements of vector analysis, $L_p$-spaces of vector fields and related Sobolev spaces. These tools are then employed to…
C. Akemann and G. Pedersen defined three concepts of semicontinuity for self-adjoint elements of A**, the enveloping von Neumann algebra of a C*-algebra A. We give the basic properties of the analogous concepts for elements of pA**p, where…
We propose a novel fractal based interpolation scheme termed Rational Cubic Trigonometric Zipper Fractal Interpolation Functions (RCTZFIFs) designed to model and preserve the inherent geometric property, positivity, in given datasets. The…
We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are…
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…