bio | website | |
---|---|---|
location | ||
age | ||
visits | member for | 2 years, 9 months |
seen | Dec 23 at 19:10 | |
stats | profile views | 2,585 |
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
deleted 1 character in body |
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?
added 1 character in body |
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
added 455 characters in body |
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
edited title |
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 $(\sharp)$. |