Related papers: Some remarks about Cantor sets
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
These are notes from a basic course in Several Complex Variables
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
These informal notes briefly discuss Fourier inversion in terms of Gauss--Weierstrass kernels and summability.
These notes present an approach to obtaining the basic operations of addition and multiplication on the natural numbers in terms of elementary results about commutative monoids.
Four constructions result from a desire to create enhancements to Cantor's infinite real set cardinality. Each continues to keep Cantor's cardinality formulation in place while providing new comparisons of arbitrary infinite sets. To…
This note remarks that small-gain results for a negative feedback loop around a monotone system can be seen as consequences of results concerning an extended monotone system.
We obtain a complete description for a probability measure to be doubling on an arbitrarily given uniform Cantor set. The question of which doubling measures on such a Cantor set can be extended to a doubling measure on [0; 1] is also…
In this article we are interested in a differential inclusion defined by an isotropic compact set.
It is shown that (1) if a good set has finitely many related components, then they are full, (2) loops correspond one-to-one to extreme points of a convex set. Some other properties of good sets are discussed.
In this article, we consider the concept of the decay of the Favard length of $\varepsilon$-neighborhoods of purely unrectifiable sets. We construct non-self-similar Cantor sets for which the Favard length decays arbitrarily with respect to…
This paper examines the possibilities of extending Cantor's two arguments on the uncountable nature of the set of real numbers to one of its proper denumerable subsets: the set of rational numbers. The paper proves that, unless certain…
In this paper, we define a soft somewhat open set using the soft interior operator. We study main properties the class of soft somewhat open sets that is contained in the class soft somewhere dense sets. Then, we introduce the classes of…
A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.
We show that a topological Cantor set in the line has at most countably many real-analytic, onto self-maps.
In \cite{ZW}, the notion of homogenous perfect set as a generalization of Cantor type sets is introduced. Their Hausdorff, lower box-counting, upper box-counting and packing dimensions are studied in \cite{ZW} and \cite{WW}. In this paper,…
The present article is devoted to some examples of functions whose arguments represented in terms of certain series of the Cantor type.
This is a short survey of amenable equivalence relations.
We study experimentally systems of orthogonal polynomials with respect to self-similar measures. When the support of the measure is a Cantor set, we observe some interesting properties of the polynomials, both on the Cantor set and in the…
These are the notes from my courses on the arithmetic of quadratic forms.