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Harmonic analysis is a generalisation of Fourier analysis that studies the properties of functions. Check out this tag for abstract harmonic analysis (on abelian locally compact groups), or Euclidean harmonic analysis (eg, Littlewood-Paley theory, singular integrals). It also covers harmonic analysis on tube domains, as well as the study of eigenvalues and eigenvectors of the Laplacian on domains, manifolds and graphs.

23 votes
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1k views

Laplace Transform in the context of Gelfand/Pontryagin

Questions: Is there a class of objects (presumably related to locally compact abelian groups) for which the quasi-characters canonically generalize the Laplace transform? If not, is there a generaliz …
11 votes
0 answers
363 views

Carleson's Theorem on Manifolds

Let $M$ be an oriented, compact, differentiable manifold with some Riemmanian metric $g$, so that $(M,g)$ has a nice volume form and one can define $L^2(M,g)$ as the completion of $C^\infty(M)$ under …