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1d
revised Dual of Banach-valued $L^p$
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2d
asked Dual of Banach-valued $L^p$
Jan
27
comment Surjectivity of curl
@Khavkine I think that Hachino has settled the question. Thanks for caring about this question.
Jan
27
comment Surjectivity of curl
Thanks for this very nice counterexample. The vanishing of the mean (i.e. $\hat \nu(0)=0$) that I required in the question above is certainly necessary, but as you have just pointed out is not sufficient. All moments should vanish, this is an elegant addendum to Poincaré Lemma.
Jan
18
answered Decompose the Laplacian
Jan
18
comment Surjectivity of curl
Thanks for your answer. However, I doubt that $v$ in the Schwartz space implies that $w$ is also in the Schwartz space. With $\mathbb P$ standing for the Leray projector, $\mathbb P$ is the matrix Fourier multiplier $curl^2(-\Delta)^{-1}$. What you wrote is $v=Pv=curl(curl(-\Delta)^{-1})v$ and you take $w=curl(-\Delta)^{-1})v$. Now there is a priori a singularity at $\xi=0$, that should be gotten rid of.
Jan
17
asked Surjectivity of curl
Jan
15
answered Witten index non-trivial in the context of Quantum Mechanics?
Jan
6
answered Transforming a recurrence to the product of two other recurrences
Jan
6
answered Examples of potentials for which Schrödinger equation lacks discrete points in continuous spectrum
Dec
22
answered Application of Egorov's Theorem for Pseudodifferential Operators
Dec
14
answered Morse lemma with least amount of regularity.
Dec
10
answered Solution of a second order nonlinear ode
Dec
10
answered Local fractional Sobolev inequality
Dec
8
comment Extension of solutions of PDEs with constant coefficients
I should have made my answer more precise, since it deals indeed with real analyticity (I have modified my answer). Of course, ellipticity alone does not imply the sought property globally in $\mathbb C^n$: take for instance for $n=1$, $\frac{\partial}{\partial z}$ and the elliptic equation $\frac{\partial u}{\partial z}=0$, which has no (non-trivial) holomorphic function as a solution.
Dec
8
revised Extension of solutions of PDEs with constant coefficients
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Dec
8
answered Extension of solutions of PDEs with constant coefficients
Dec
8
comment Is there a compactly supported function that its Fourier transfrom vanishes at given n real points?
I agree with your answer, but it could not be generalized to an infinite number of zeroes, a natural extension of the question. The Weierstrass factorization theorem allows to construct entire functions with prescribed zeroes and in some case these functions could be of exponential type, thus with compactly supported Fourier transforms, e.g $\sin z$.
Dec
6
revised Is there a compactly supported function that its Fourier transfrom vanishes at given n real points?
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