Potpourri, 2
These notes are connected to a "potpourri" topics class and deal with some basic issues involving norms and convexity.
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arXiv subjects
Stephen Semmes
Publications and source records attributed to Stephen Semmes.
Notes on commutative algebra and harmonic analysis
Fourier series with absolutely summable coefficients provide a classical example of a commutative Banach algebra, and these notes are concerned with this and related matters.
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Notes on groups and representations
These informal notes concern some basic themes of harmonic analysis related to representations of groups.
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Notes on functions on the unit disk
In these notes we consider power series representations of functions on the unit disk in the complex plane which define harmonic and holomorphic functions and related matters concerning boundary values, Poisson kernels, and so on.
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Some notes on harmonic and holomorphic functions
These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, using quaternions and Clifford algebras in higher dimensions. The main themes are weak solutions, the mean-value property, and subharmonicity.
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A beginner's guide to analysis on metric spaces
These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.
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Some topics in complex and harmonic analysis, 4
These notes briefly consider convolutions of tempered distributions with functions in the Schwartz class.
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Some topics in complex and harmonic analysis, 5
These notes deal with a few properties of convolutions in the role of approximations to the identity.
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Some topics in complex and harmonic analysis, 3
These notes briefly consider some aspects of the Schwartz class of rapidly decreasing smooth functions, tempered distributions, and harmonic functions of polynomial growth.
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Notes on normed algebras, 5
These notes briefly discuss finite-dimensional algebras with involutions, self-adjoint elements, and so on.
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Notes on normed algebras, 4
These notes deal with algebras equipped with an involution and related matters.
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Notes on normed algebras
These notes deal with finite-dimensional normed algegras, some basic examples, and the definition of the spectrum.
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Notes on normed algebras, 2
In these notes we focus on commutative finite-dimensional normed algebras and some basic examples.
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Notes on normed algebras, 3
In these notes we briefly consider various situations related to infinite commutative semigroups, connected to convolutions and Fourier transforms.
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Some topics in complex and harmonic analysis, 2
These notes are concerned with Abel sums and connections with analytic extensions of Fourier integrals.
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Elements of harmonic analysis, 5
These notes are concerned with the Schwartz class of rapidly decreasing smooth functions on R^n, Fourier transforms, etc.
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Some topics in complex and harmonic analysis
These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.
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