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bio website math.purdue.edu/~eremenko
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Math Professor

May
26
awarded  Necromancer
May
22
comment Estimates for derivatives of a positive discrete harmonic function
The old book of F. Spitzer, Principles of random walk, almost surely contains this, but I do not have it beside me at the moment.
May
22
awarded  Nice Answer
May
15
comment What questions should -ologists of mathematics ask, in order to improve maths researcher training?
"ologists" from social and humanity science should not interfere in training of research mathematicians, the thing which they do not understand.
May
14
comment Estimates for derivatives of a positive discrete harmonic function
Why don't you just repeat the proof for ordinary harmonic functions, using Harnack and Poisson's formula. All these things are available in the discrete setting.
May
14
answered Oscillation of subharmonic functions of slow growth
May
11
comment Physics that needs “new” math
There are plenty of examples when new math was created by physicists or for the needs of physics. A VERY large part of Mathematics was created to answer the concerns of physicists.
May
10
comment The Lebesgue measure of the low level sets of the two-dimmension Fourier transform of a compactly supported function
Then the Fourier transform is bounded and equals $1$ at $0$. Cartan's lemma evidently works in any dimension.
May
10
comment The Lebesgue measure of the low level sets of the two-dimmension Fourier transform of a compactly supported function
If $f\equiv 0$ what estimate do you obtain?
May
10
comment The Lebesgue measure of the low level sets of the two-dimmension Fourier transform of a compactly supported function
I am not discussing how to solve. State your question clearly. IN WHAT TERMS do you want the estimate.
May
10
comment The Lebesgue measure of the low level sets of the two-dimmension Fourier transform of a compactly supported function
Notice that your Fourier transform is an entire function of exponential type. If this is not enough for you, tell us in what terms do you want the upper bound (it is clear that it may depend on $f$ as stated).
May
7
comment how wiggly is a generic level set?
@ragnar: the eigenvalue of $y(x)=\sin(kx)$ is $\lambda=-k^2$. I mean in the sense $y''=\lambda y$. So it is just the question of notation: what you call spectrum, the set of $k$ or the set of $k^2$.
May
6
comment how wiggly is a generic level set?
@Ragnar: I added the answer.
May
5
revised how wiggly is a generic level set?
added 815 characters in body
May
2
comment Not especially famous, long-open problems which anyone can understand
@Nemo: If you look at the file which I cited you find some partial results. In particular, in $R^3$, if $m_k\geq c>0$, and $\sum_k m_k/|x_k|<\infty$, there are infinitely many zeros. But convergence condition here is more restrictive than conjectured.
May
2
comment Interpolation between strongly convex functions
The answer to the modified question is still "no", even in dimension 1. Just draw a picture!
May
1
comment Interpolation between strongly convex functions
Of course not. Take $d=1$, $f$ even, increasing for $x>0$, but $g$ decreasing for $x>x_0$.
May
1
comment how wiggly is a generic level set?
On compact you have Courant's theorem. Everyting is controlled by $\sqrt{\lambda}$ where $\lambda$ is your largest allowed eigenvalue.
May
1
comment how wiggly is a generic level set?
There is no difference between a unit ball, any ball or compact region.
Apr
30
answered how wiggly is a generic level set?