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Results tagged with harmonic-analysis
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user 8857
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.
2
votes
Accepted
Maximal function on small cubes
By Holder’s inequality
$$ \frac{1}{\lvert Q\rvert}\int_{Q}V^{+}dm \leq \frac{1}{\lvert Q\rvert} \lvert Q\rvert^{1/q}\cdot \left(\int_{Q} \left(V^{+}\right)^{p}dm \right)^{1/p} = \left(\lvert Q\rvert^{ …
- 2,459
7
votes
Background for Hejhal's "The Selberg Trace Formula for $PSL(2, \mathbb{R})$
Well, the modern viewpoint relays on the interpretation of "fourier transform" (in any generalized fashion you like to define "fourier transform") in representation-theoretic language.
As a consequenc …
- 2,459
2
votes
Accepted
Basic question on minimal flows
Your question is about a theorem of Furstenberg.
About the definitions - obviously every periodic orbit is minimal, if exists, hence in the case the action is minimal, you won't have any periodic orb …
- 2,459