bio | website | |
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location | ||
age | ||
visits | member for | 2 years, 7 months |
seen | Oct 6 at 15:28 | |
stats | profile views | 2,461 |
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 $(\sharp)$. |
Sep 24 |
revised |
Generalized Hardy-Littlewood-Sobolev Inequality
edited body |
Sep 23 |
asked | Generalized Hardy-Littlewood-Sobolev Inequality |
Sep 19 |
comment |
For what nonnegative measures $\mu$ does $\mu*e^{-|\cdot|}\in L^{\infty}$?
$\hat \mu\hat f$ is a complex (valued) measure on the real line with finite total mass. |
Sep 18 |
comment |
For what nonnegative measures $\mu$ does $\mu*e^{-|\cdot|}\in L^{\infty}$?
$\hat \mu\hat f$ should be a measure on the real line with finite total mass. |
Sep 17 |
revised |
For what nonnegative measures $\mu$ does $\mu*e^{-|\cdot|}\in L^{\infty}$?
added 220 characters in body |
Sep 17 |
comment |
For what nonnegative measures $\mu$ does $\mu*e^{-|\cdot|}\in L^{\infty}$?
In that case, $\hat \mu=\mu$ by Poisson summation formula. It is probably possible to weaken my requirement to $$\hat \mu\hat f\text{ is a measure with a finite total mass}.$$ If $f=e^{-\vert x\vert}$, you find $\hat f\hat \mu$ with finite mass since $\sum_{n\ge 1}\frac{1}{n^2}<+\infty$. |
Sep 17 |
revised |
For what nonnegative measures $\mu$ does $\mu*e^{-|\cdot|}\in L^{\infty}$?
added 508 characters in body |
Sep 17 |
comment |
For what nonnegative measures $\mu$ does $\mu*e^{-|\cdot|}\in L^{\infty}$?
I have added a complement to my answer above. |
Sep 16 |
answered | For what nonnegative measures $\mu$ does $\mu*e^{-|\cdot|}\in L^{\infty}$? |
Sep 15 |
comment |
Eigenstates of Fourier transformation
@Christian Remling: yes, of course, thanks. |
Sep 15 |
comment |
Eigenstates of Fourier transformation
@Robert Israel: yes, but I would like a somewhat more explicit description yielding in particular the Poisson summation formula. The latter formula is not exactly a triviality and to provide an algebraic proof would be interesting. |
Sep 15 |
comment |
Eigenstates of Fourier transformation
The question is not Hilbertian, but on $\mathcal S'$: I want also to include the Poisson summation formula. |
Sep 15 |
asked | Eigenstates of Fourier transformation |
Sep 10 |
awarded | ap.analysis-of-pdes |
Sep 9 |
comment |
Nonharmonic solutions of Laplace's equation
My (Bazin's) answer and Liviu Nicolaescu's answer are correct and contradict George Lowther's answer. The point is to decide what means $\Delta u=0$. In the sense of distributions, it is clear and both answers mentioned above give a clearcut result. Now if you accept the "counterexample" above which is missing a point, the Laplace equation is not satisfied in the distribution sense. |
Sep 8 |
awarded | Revival |
Sep 7 |
answered | Extension of pseudodifferential operators |
Sep 5 |
comment |
Are Besov spaces $B^{s}_{p,q}$ invariant under Fourier transform?
The equality $\sum_{k\ge 0}\phi_k(\xi)=1$ is equivalent to $\sum_{k\ge 0}\phi_k(D)=Id.$ |