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Results tagged with harmonic-analysis
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user 163172
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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$l^2(L^p)$ Decoupling constant of congruent tubes
Demeter's book Fourier Restriction, Decoupling, and Applications give a principle that one cannot decouple in a direction where the manifold is flat. Which is the below proposition:
Proposition 9.5 L …
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$l^2(L^p)$ Decoupling constant of congruent tubes
Thanks to Willie Wong and Ben Johnsrude.
Now I set $T=[0,1]\times B_{n-1}(0,1)=\left\{(x_1,x^*)\in\mathbb{R}^n: x_1\in[0,1],x^*\in B_{n-1}(0,1)\right\}$, here $B_{n-1}(0,1)$ is the unit ball in $\math …
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