相关论文: Some remarks about Cantor sets

The present article is devoted to certain examples of functions whose argument represented in terms of Cantor series.

We investigate some self-similar Cantor sets $C(l,r,p)$, which we call S-Cantor sets, generated by numbers $l,r,p \in \mathbb{N}$, $l+r<p$. We give a full characterization of the set $C(l_1,r_1,p)-C(l_2,r_2,p)$ which can take one of the…

This survey synthesizes the principal descriptive set-theoretic perspectives on deterministic Cantor sets on the real line and charts directions for future study. After recounting their historical genesis and compiling an up-to-date…

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

A few aspects of self-similarity related to complementary components of closed subsets of R^n are briefly discussed.

These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.

Some formulas and speculations are presented relative to integrable systems and quantum mechanics.

This short note contains elementary evaluations of some Euler sums.

The special case of closed subsets of C^n is briefly discussed.

These informal notes deal with a number of questions related to sums and integrals in analysis.

Remarks relating the various notions of corks.

We consider approximately greater than relations on fuzzy sets and discuss their properties.

The note complements topological aspects of the theory of chiral algebras.

These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

Some aspects of Cauchy integrals on sets with dimension larger than 1 are briefly discussed.

We give new arguments for sums and products of sufficient numbers of arbitrary central Cantor sets to produce large open intervals. We further discuss the same question for $C^1$ images of such central Cantor sets. This gives another…

The complement of a Cantor set in the complex plane is itself regarded as a Riemann surface of infinite type. The problem is the quasiconformal equivalence of such Riemann surfaces. Particularly, we are interested in Riemann surfaces given…

We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smaller than its Hausdorff dimension. Some Hausdorff measure…

In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.

These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.