15 citations · 27 across the 7 of their papers we have counts for
8 papers
Arbitrarily Close for Summer 2022 Analysis
John A. Rock
The kernel of analysis, to me anyway, is the following idea: A point is arbitrarily close to a set if every neighborhood of the point intersects the set. Defining ``arbitrarily clo…
A Lecture on Integration by Parts
John A. Rock
Integration by parts (IBP) has acquired a bad reputation. While it allows us to compute a wide variety of integrals when other methods fall short, its implementation is often seen…
A survey of complex dimensions, measurability, and the lattice/nonlattice dichotomy
Kristin Dettmers, Robert Giza, Christina Knox +2
The theory of complex dimensions of fractal strings developed by Lapidus and van Frankenhuijsen has proven to be a powerful tool for the study of Minkowski measurability of fractal…
Box-counting fractal strings, zeta functions, and equivalent forms of Minkowski dimension
Michel L. Lapidus, John A. Rock, Darko Žubrinić
We discuss a number of techniques for determining the Minkowski dimension of bounded subsets of some Euclidean space of any dimension, including: the box-counting dimension and equ…
Multifractal analysis via scaling zeta functions and recursive structure of lattice strings
Rolando de Santiago, Michel L. Lapidus, Scott A. Roby +1
The multifractal structure underlying a self-similar measure stems directly from the weighted self-similar system (or weighted iterated function system) which is used to construct…
Partition zeta functions, multifractal spectra, and tapestries of complex dimensions
Kate E. Ellis, Michel L. Lapidus, Michael C. Mackenzie +1
For a Borel measure and a sequence of partitions on the unit interval, we define a multifractal spectrum based on coarse Holder regularity. Specifically, the coarse Holder regulari…