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Results tagged with harmonic-analysis
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user 96950
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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When are solutions of the Schrödinger equation radial?
Let $S$ be a nonnegative self-adjoint operator on a complex Hilbert space $X$. (For example, $X$ consists of functions on $\mathbb R^d$; it could be $L^2(\mathbb R^d), \dot{H}^2(\mathbb R^d)$, etc. …
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$(i\partial_t)^{\frac{1}{2}} e^{it\Delta} f = (-\Delta )^{\frac{1}{2}} e^{it\Delta} f$?
Put $\langle x \rangle ^s = (1 + |x|)^{1/2},$ and $|\nabla |^s $ denotes the Fourier multiplier with symbol $|\xi|^s$, that is, $\widehat{|\nabla |^s f} = |\xi|^s \hat{f}.$
Put $ \langle \nabla \r …
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