Analysis on disconnected sets
Some aspects of analysis on disconnected sets are briefly discussed, more along the lines of regions with infinitely many components than Cantor sets.
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arXiv subjects
Stephen Semmes
Publications and source records attributed to Stephen Semmes.
Some remarks about Cauchy integrals and fractal sets
Some aspects of Cauchy integrals on sets with dimension larger than 1 are briefly discussed.
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A few remarks about operator theory, topology, and analysis on metric spaces
Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals.
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Some algebraic notions related to analysis on metric spaces
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
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Some aspects of algebraic topology: An analyst's perspective
These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.
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Mappings and spaces, 2
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
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Adventures in harmonic analysis
These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.
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Notes on p-adic numbers
These notes deal with some basic notions related to p-adic numbers and functions of p-adic numbers.
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Notes on Lie algebras and Lie groups
These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.
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Potpourri, 11
These informal notes deal with some topics related to analysis on metric spaces.
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Potpourri, 10
These notes, associated with a topics course, are largely concerned with Hausdorff measures and a class of metric spaces which behave like Cantor sets.
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Potpourri, 9
These notes, associated with a topics course, are concerned with Hausdorff measures and Lipschitz functions on metric spaces.
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Potpourri, 8
These notes, associated with a topics course, deal with some special features of summability and supremum norms which are often useful.
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Potpourri, 6
These notes, associated with a topics course, are concerned with some general methods related to norms and linear transformations.
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Potpourri, 7
These notes, associated with a topics course, deal with some special cases involving norms and linear transformations.
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Potpourri, 5
These notes deal with some topics related to limits of norms, functions on the unit circle, and so on.
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Potpourri, 4
These notes, connected to a "potpourri" topics course currently underway, are concerned with some interrelated themes of polynomials, functions on the unit circle or interval, and norms.
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Potpourri, 3
These notes are connected to a "potpourri" topics class and deal with some special cases of norms of various objects which arise in classical analysis.
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