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Stephen Semmes

Publications and source records attributed to Stephen Semmes.

At least 91 records · Page 5Linked to original sources
arXiv2004

Elements of harmonic analysis, 3

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

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arXiv2004

Elements of harmonic analysis, 2

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

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arXiv2004

Elements of harmonic analysis

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

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arXiv2003

Some remarks about metric spaces

The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are concerned with some particular situations involving sub-Riemannian geometry, hyperbolic groups, and p-adic numbers.

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arXiv2003

Some notes about matrices, 4

In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.

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arXiv2003

Some notes about matrices, 5

This short survey reviews some aspects of spaces of positive-definite self-adjoint linear transformations on R^n and on C^n, including the standard Riemannian metric and the relation with the exponential mapping acting on self-adjoint linear transformations, which indeed leads to geodesics of positive-definite linear transformations.

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arXiv2003

Some notes about matrices, 2

Here we briefly discuss lattices in Euclidean spaces and spaces of lattices, which are basic objects that can be described in terms of matrices and are important settings in classical analysis.

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arXiv2003

Some notes about matrices, 3

Here we briefly describe some topics along the lines of projective spaces and related geometric constructions connected to linear algebra, which provide fundamental examples in classical geometry and analysis.

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arXiv2003

Some remarks about metric spaces, 2

This short survey has been prepared in connection with the workshop on discrete metric spaces and their applications at Princeton, August, 2003, and tries to convey some of the ways that one might look at functions on metric spaces in harmonic analysis, in terms of behavior at different scales and locations in the space.

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arXiv2003

Notes on topological vector spaces

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.

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arXiv2003

Happy fractals and some aspects of analysis on metric spaces

By a "happy fractal" we mean a metric space with bounded geometry in the sense of a doubling condition and a lot of paths of finite length, so that any pair of points can be connected by a path whose length is less than or equal to a constant times the distance between the two points. In these notes we consider some examples, related notions, and other aspects of analysis on metric spaces. This includes Lipschitz functions of some positive order and the special class of functions known as "atoms" which are related to singular integral operators.

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arXiv2003

Notes on metrics, measures, and dimensions

These notes deal with metric spaces, Hausdorff measures and dimensions, Lipschitz mappings, and related topics. The reader is assumed to have some familiarity with basic analysis, which is also reviewed.

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