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Results tagged with harmonic-analysis
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user 173418
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.
3
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answers
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What is standard continuity argument for well-posedness?
Motivation: I'm trying to understand the proof of Theorem 3.1 in Antonelli, Saut, and Sparber - Well-Posedness and averaging of NLS with time-periodic dispersion management. Though in the following I' …
- 325
1
vote
0
answers
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How to show the solution map of NLS is not smooth?
Let $u(\delta, t)$ satisfy
$$iu_t +\Delta u+ |u|^{2k}u=0, \quad u(0)=\delta v_0$$
Note that the mapping:
$$\delta v_0\mapsto u(\delta, t)= S(t)(\delta v_0)-i\int_0^tS(t-\tau)(|u|^{2k}u)(\tau)d\tau $$
…
- 325