相关论文: Some remarks about Cantor sets

These informal notes deal with p-adic versions of Heisenberg groups and related matters.

In this paper we discuss several variations and generalizations of the Cantor set and study some of their properties. Also for each of those generalizations a Cantor-like function can be constructed from the set. We will discuss briefly the…

In these informal notes, we continue to explore p-adic versions of Heisenberg groups and some of their variants, including the structure of the corresponding Cantor sets.

These informal notes concern some basic themes of harmonic analysis related to representations of groups.

In this short note, we discuss the topology of Diophantine numbers, giving simple explicit examples of Diophantine isolated numbers (among those with same Diophantine constatnts), showing that, Diophantine sets are not always Cantor sets.…

We present some informal remarks on aspects of relativistic quantum computing.

We give lower bounds for the Hausdorff dimensions of some model Furstenberg sets.

These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.

Cantor sets of integers have a rich set of arithmetic combinatorial properties. We consider classical Cantor sets, with a base and a fixed set of allowed digits. For such sets, we (a) give examples of such sets that satisfy the intersective…

These notes, associated with a topics course, are largely concerned with Hausdorff measures and a class of metric spaces which behave like Cantor sets.

We construct a combinatorially large measure zero subset of the Cantor set.

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

These informal notes deal with some topics related to analysis on metric spaces.

We give some examples of IFSs with overlap on the interval such that the semigroup action they give rise to has a minimal set homeomorphic to the Cantor set.

These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.

These informal notes are concerned with sums and averages in various situations in analysis.

Some aspects of analysis on disconnected sets are briefly discussed, more along the lines of regions with infinitely many components than Cantor sets.

Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the Monthly, despite its intense coverage of quotient sets over the years.

These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.