Related papers: Fractal Interpolation over Curves
Building upon Bennett's and Grosse-Erdmann's ideas falling under the conceptual umbrella of factorization of inequalities, we propose a unified approach towards the structure of certain Banach ideal spaces defined in terms of the least…
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
The essence of Stahl-Gonchar-Rakhmanov theory of symmetric contours as applied to the multipoint Pad\'e approximants is the fact that given a germ of an algebraic function and a sequence of rational interpolants with free poles of the germ,…
We prove that an interpolation pair of Banach lattices is uniquely determined by the collection of intermediate spaces with the property that these are interpolation spaces for positive operators. A correspondent result for exact…
The known duality of the space of Bloch complex-valued functions on the open complex unit disc $\mathbb{D}$ is addressed under a new approach with the introduction of the concepts of Bloch molecules and Bloch-free Banach space of…
A novel focusing structure with fractal properties is presented. It is a photon sieve in which the pinholes are appropriately distributed over the zones of a fractal zone plate. The focusing properties of the fractal photon sieve are…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
When information is spatially repeated in self-similar fractal beam patterns, only a portion of the diffracted beam is needed to reconstruct the kernel data. What is unique to a fractal-encoding scheme is that the image demultiplexing…
We introduce a novel frame-interpolation-based method for slice imputation to improve segmentation accuracy for anisotropic 3D medical images, in which the number of slices and their corresponding segmentation labels can be increased…
Starting with a substitution tiling, we demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles have fractal boundary. We show…
A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the…
The complex method of interpolation, going back to Calder\'on and Coifman et al., on the one hand, and the Alexander-Wermer-Slodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of…
We formalize a technique for embedding Riemann sufraces properly into \C^2, and we generalize all known embedding results to allow interpolation on prescribed discrete sequences.
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
We present the error analysis of Lagrange interpolation on triangles. A new \textit{a priori} error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on…
This article studies divergence of multivector fields on Banach manifolds with a Radon measure. The proposed definition is consistent with the classical divergence from finite-dimensional differential geometry. Certain natural properties of…
Cohomology fractals are images naturally associated to cohomology classes in hyperbolic three-manifolds. We generate these images for cusped, incomplete, and closed hyperbolic three-manifolds in real-time by ray-tracing to a fixed visual…
A new approach for simulating flows over complex geometries is developed by introducing an accurate virtual interpolation point scheme as well as a virtual local stencil approach. The present method is based on the concept of point…
With the increased use of virtual and augmented reality applications, the importance of point cloud data rises. High-quality capturing of point clouds is still expensive and thus, the need for point cloud super-resolution or point cloud…
We study multiple sampling, interpolation and uniqueness for the classical Fock space in the case of unbounded mul-tiplicities.