arXiv subjects
Publications and source records attributed to Stephen Semmes.
There seems to be quite a bit of room for interesting things related to surfaces M in C^m with real dimension m which are totally real and aspects of several complex variables on C^m around M. A basic case occurs when m = 1, with Cauchy integral operators along curves, holomorphic functions on the complements of curves, and so on. In the present article we briefly indicate a few points concerning these matters.
This paper briefly discusses some questions with analytical and topological aspects, with hopefully some useful references on both sides.
In this short survey we look at a few basic features of p-adic numbers, somewhat with the point of view of a classical analyst. In particular, with p-adic numbers one has arithmetic operations and a norm, just as for real or complex numbers.
A basic point about hyperbolic groups is that they have "spaces at infinity" which are spaces of homogeneous type in the sense of Coifman and Weiss, and with a lot of self-similarity coming from the group. This short survey deals with some of the notions involved.
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
In these notes we discuss some relations between complex analysis (derivatives of Cauchy integrals) and curvatures of curves and surfaces. In higher dimensions the Cauchy integrals are based on generalizations of complex analysis using quarternions or Clifford algebras. These topics came up in "Analysis of and on Uniformly Rectifiable Sets" (with Guy David, American Mathematical Society, 1993), and here we describe some of the basic points involved. A presentation based on this paper was made at the AMS Special Session "Surface Geometry and Shape Perception" (Hoboken, 2001).
This is brief and hopefully friendly, with basic notions, a few different perspectives, and references with more information in various directions.
This article discusses several matters related to Sobolev, Poincare, and isoperimetric inequalities in various settings.
This report tries to give a brief overview of a number of the mathematical activities during the trimestre mentioned in the title.
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic geometry as on a graph, for instance. Of course this is a common theme which is considered in numerous settings. From an analysts' perspective, compact groups, their representations, and more general topological groups and their representations are basic objects of study. Finite groups are like groups which are especially compact, and with some extra structure. As long as one considers finite groups and finite-dimensional vector spaces, one might as well consider general underlying fields k too. This includes p-adic fields, which are quite interesting for analysis.
This is a brief survey which reviews some traditional themes in harmonic analysis and some more recent areas of activity, connected to "analysis on fractals" in particular.
In this brief survey we give an introduction to some aspects of "atoms" on metric spaces and their connection with linear operators.
These are some basic notes concerning Holder and Lipschitz classes on metric spaces.
The "potentials" being considered are analogues of classical Riesz potentials of order 1, and the idea is to look at how they might map L^p spaces into Sobolev spaces in various settings.
This is a kind of introduction to some basic topics in analysis, some of which would be covered in standard graduate courses, and some not. However, an important difference is that not much in the way of prerequisites are needed, beyond linear algebra and beginning analysis. In particular, this should be accessible to undergraduates or readers whose main focus is not necessarily pure mathematics. One could easily accommodate Lebesgue integrals and so forth if one wanted to, but they are not really needed.
Contents 1 Mappings and distortion 2 The mathematics of good behavior much of the time, and the BMO frame of mind 3 Finite polyhedra and combinatorial parameterization problems 4 Quantitative topology, and calculus on singular spaces 5 Uniform rectifiability Appendices A Fourier transform calculations B Mappings with branching C More on existence and behavior of homeomorphisms D Doing pretty well with spaces which may not have nice coordinates E Some simple facts related to homology