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seen Dec 23 at 19:10

Dec
22
answered Application of Egorov's Theorem for Pseudodifferential Operators
Dec
14
answered Morse lemma with least amount of regularity.
Dec
13
comment Riemann Hypothesis and the Maximum Principle
The function $\zeta$ is meromorphic with a single simple pole at $s=1$, so is indeed holomorphic in a neighborhood of the critical line. I do not understand your first "would imply".
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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Dec
6
answered Is there a compactly supported function that its Fourier transfrom vanishes at given n real points?
Dec
5
revised Complex transport equation
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Dec
5
answered Complex transport equation
Nov
30
comment Notion of solution of pde
The linear part of the equation $iu_t+\Delta u$ is easy to define for a distribution. However, taking $F(u)=u^2$ would require essentially that $u(t)$ belongs to an algebra, which is not the case for $H^1(\mathbb R^n)$ when $n\ge 2$: this means that I do not understand how the equation could make sense without some additional assumptions of regularity for $u$, e.g. $H^{\epsilon +n/2}(\mathbb R^n)$.
Nov
24
comment Continuity in Banach space for non-linear maps
Nice. You mean that $f$ is scalar-valued and defined by $\sum_{n\ge 1}nx_n^n$. Your sum on $n$ does not converge, say if $x_1=1$.
Nov
24
revised Continuity in Banach space for non-linear maps
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Nov
21
asked Continuity in Banach space for non-linear maps
Nov
8
answered Paraproduct and Fourier series
Oct
6
asked Discrete versus Continuous Hilbert Transform
Sep
24
comment Generalized Hardy-Littlewood-Sobolev Inequality
@John Bentin : No, this is the same condition as the one for Young's inequality $L^p\ast L^q\subset L^r$ under $(\sharp)$.