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seen Oct 6 at 15:28

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 $\sum_{k\ge 0}\phi_k(D)=Id.$