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Results tagged with harmonic-analysis
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user 512768
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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$L^\infty-L^1$ norm of an oscillatory integral operator
Let $\lambda>1$, $x,y\in [0,1]$, and $K_\lambda(x,y)=(1+\lambda|x-y|)^{-2}e^{i\lambda|x-y|}$. Consider the operator
$$T_\lambda f(x)=\int_0^1 K_\lambda(x,y)f(y)dy.$$
We want to precisely estimate the …
- 31