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Results tagged with harmonic-analysis
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user 500582
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.
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Eigenfunction expansion theorem for general manifold for smooth functions
The question starts with the well known facts that: if $f$ is a smooth function on $S^1$, then its Fourier series converges to it in smooth topology.
This must be true in more general setting. I have …
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