16 citations · 30 across the 7 of their papers we have counts for
7 papers
Calculating Hausdorff dimension in higher dimensional spaces
M. A. Sánchez-Granero, M. Fernández-Martínez
In this paper, we prove the identity , where denotes Hausdorff dimension, , and…
Irreducible fractal structures for Moran's type theorems
M. A. Sánchez-Granero, M. Fernández-Martínez
In this paper, we characterize a novel separation property for IFS-attractors on complete metric spaces. Such a separation property is weaker than the strong open set condition (SO…
Generalizing Moran's Theorem
M. Fernández-Martínez, Juan L. G. Guirao, M. A. Sánchez-Granero
This work is aimed by the spirit of 1946 Moran's Theorem, which ensures that both the box and the Hausdorff dimensions for any attractor could be calculated as the solution of an e…
Optimal sampling patterns for Zernike polynomials
D. Ramos-Lopez, M. A. Sanchez-Granero, M. Fernandez-Martinez +1
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the co…
Counterexamples for IFS-attractors
Magdalena Nowak, Manuel Fernandez-Martinez
In this paper, we deal with the part of Fractal Theory related to finite families of (weak) contractions, called iterated function systems (IFS, herein). An attractor is a compact…
Fractal Dimension for Fractal Structures: A Hausdorff Approach
M. A. Sánchez-Granero, Manuel Fernández-Martínez
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definiti…