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Apr
27
comment range of singular values of sub-matrices
By playing around with the case when $A$ is diagonal and $E$ is a coordinate subspace, one can also see that these interlacing inequalities are sharp.
Apr
26
comment Probability theory without deductive closure
Boaz Barak has recently blogged about a computational approach to belief (in which deduction is computationally expensive) which may eventually serve as a suitable model for this sort of reasoning, although it is not yet fully formalised: windowsontheory.org/2016/04/13/… .
Apr
24
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Apr
24
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Apr
24
answered Is there a $C_c^{\infty}( \mathbb{R}^d)$ function whose Fourier transform we can explicitly write down?
Apr
23
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Apr
23
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Apr
23
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Apr
22
comment Vorticity form of Euler equation: What about harmonic part?
In the specific case of the 2-torus, it appears that momentum conservation will keep the harmonic component of $\eta$ fixed, but this seems special to the $2$-torus. It may well be that one cannot write the Euler equations purely in terms of the vorticity for more general compact domains, but one must instead consider a coupled system between the vorticity and the harmonic component.
Apr
22
comment Vorticity form of Euler equation: What about harmonic part?
Why must ${\mathcal L} h$ vanish?
Apr
22
comment Two questions on Elias Stein paper (1976)
I think the OP is referring to one of my first papers, ams.org/mathscinet-getitem?mr=1420506 , though I don't know why it would be relevant to spherical averaging.
Apr
21
comment Two questions on Elias Stein paper (1976)
It may be that the OP is interested in "variable coefficient" versions of these theorems suitable for curved manifolds such as $S^2$. In this case one can look at Chapter XI.3 of Stein's "Harmonic analysis", which basically shows that the results of Stein extend to variable coefficient settings so long as a "rotational curvature" condition is satisfied. In 2D one needs a "cinematic curvature" condition; see Chapter XI.4.D of Stein.
Apr
21
revised Two questions on Elias Stein paper (1976)
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Apr
20
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Apr
18
revised How many primes can there be in a short interval?
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Apr
11
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Apr
11
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Apr
10
revised Square root of dirac delta function
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10
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Apr
10
revised Square root of dirac delta function
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