1,785 reputation
929
bio website www-ian.math.uni-magdeburg.de/…
location Magdeburg, Germany
age 31
visits member for 4 years
seen Dec 3 at 0:15

I am an Australian mathematician.


Jul
1
answered An integral identity
Jul
1
comment An integral identity
Would you please include a description of the "brute-force" method?
Jul
1
comment Fourier series at discontinuities
@Hans I started writing my answer below before looking at the paper, but did have a vague recollection of it. It turns out that in the end, the argument is identical to that found in Chernoff's paper. Do you know if this is the original source of the argument?
Jul
1
answered Fourier series at discontinuities
Jun
21
comment Sufficient conditions for Liouville theorem
@Willie I had no intention of such a long comment exchange. I'll take anything further to chat.
Jun
21
comment Sufficient conditions for Liouville theorem
@Gortaur I was thinking of a different exponential map (too much differential geometry). It seems I was wrong about Theorem 3.5 from G&T as you rightly pointed out. It only gives the statement of Liouville's theorem if you instead of boundedness assume an achieved maximum or minimum, which is plainly silly.
Jun
21
comment Sufficient conditions for Liouville theorem
@Gortaur I don't see your point: $e^x$ is bounded below and achieves a minimum at zero. It is not bounded above.
Jun
21
comment Sufficient conditions for Liouville theorem
@Gortaur I think you need to check the conditions of Theorem 3.5 from G&T. In particular those on the elliptic operator. For that function, you need to have $c<0$, and so only reach a contradiction for functions which are bounded above. (As you have observed.)
Jun
21
comment Sufficient conditions for Liouville theorem
@Gortaur If a function is bounded above (or below) on $\mathbb{R}^n$ then it achieves its maximum (or minimum) on it also (not at infinity).
Jun
21
comment Sufficient conditions for Liouville theorem
@Theo Thanks for the reference. I was aware of this proof but not aware of the reference!
Jun
21
comment Sufficient conditions for Liouville theorem
@Gortaur, apologies, it wasn't clear to me that you could not find the original reference. The proof of the classical version is quite simple and does indeed follow from the maximum principle (in a sense).
Jun
21
comment Sufficient conditions for Liouville theorem
If you are just after the classical version, then you may be satisfied with Theorem 3.5 from Gilbart and Trudinger.
Jun
21
comment Sufficient conditions for Liouville theorem
You might want to improve the question by stating the excact version of Liouville's theorem you are referring to (there are several), which script or book which you are reading, and a statement of the strong maximum principle.
Jun
20
comment Collatz finally solved?
This just appeared in a newspaper here in Germany as a purported solution. I'm sorry to read that it is so plainly false :(.
Jun
11
awarded  Nice Answer
Jun
2
comment How to integrate by parts in spherical coordinates
Are you still looking for some more information about this Nanoc? If you could explain what is sill missing for you, perhaps I could help.
Jun
1
answered Can I use Ravi Vakil's way of learning for elementary subjects?
May
31
comment Coordinate-free techniques in Lagrangian mechanics
@Jor I take your point, but would like to also point out that if Akater is indeed still learning English and used the word inadvertently, then it is much better to become aware of standard (and dare I say it, correct) usage. I have yet to hear "somewhy" spoken.
May
31
comment Coordinate-free techniques in Lagrangian mechanics
@Joriki, Akater: It's not really a word. The expression you are looking for is "for some reason".
May
30
comment How to prove that the Cantor ternary function is not weakly differentiable?
The last part of the argument doesn't seem correct. The function $f(x) = 1/2$ for $x\in[0,1/2)$ and $f(x) = 2x-1/2$ seems to be a counterexample to the last claim.