3,037 reputation
1247
bio website regularize.wordpress.com
location Braunschweig, Germany
age 36
visits member for 4 years
seen 54 mins ago

Professor at TU Braunschweig.

Area: Inverse problems, regularization theory, applied functional analysis, mathematical image processing.


5h
comment Are there examples of families of objects which are canonically isomorphic, but where diagrams of canonical isomorphisms don't commute?
In the first paragraph I thought that the unit square would be $[0,1]^2$ but then I realized that you had $[-1,1]^2$ in mind.
1d
comment What should be considered a finite size of an infinite dimensional space?
I second Yemon's comment. You may note that in Yemon's example the natural inverse is not continuous if you equip both spaces with the natural norm of the larger space (i. e. the sup-norm).
1d
comment What should be considered a finite size of an infinite dimensional space?
My naive way of looking at this kind of problems would be to take "natural topologies" on both sets and say one is smaller than the other if one can identify the objects the small space in a natural way with the objects in the larger space and this identification is continuous. So in Yemon's example, $B$ would be indeed smaller than $A$…
2d
comment Integrals involving trigonometric functions and polynomes
Now I notice the question mark behind the formula. Maybe it's just a nitpick, but "Specify all…?" does not sound like a question to me (in contrast to "What are all…?"). Generalization per se may be a motivation but I thought you something more that this, e.g. that some integrals of this type appeared somewhere else.
2d
comment Integrals involving trigonometric functions and polynomes
I think that this would get a better response if it would come as a question and not a command and also accompanied by some motivation and more background.
2d
comment Quantitative stability: Hausdorff distance between subdifferentials
@RobertIsrael Right, it's indeed simple. Well, this simply reflects that uniform convergence does not imply convergence of the derivative (although, in principle convexity could change things but apparently it doesn't).
2d
comment Quantitative stability: Hausdorff distance between subdifferentials
Don't know of anything, but have you checked Rockafellar and Wets' "Variational Analysis"? By the way, I suspect that the situation could be different for smooth $f$ and $g$…
Oct
17
comment A fixed point problem about the iterated mappings
As the question appeared in the review queue, I started editing. Halfway through, I realized that the question does not make sense as stated… For what it's worth: The answers to your questions is: 1. $\lim f^m(x)$ does not exist (hence asking if it is in $\Omega$ or not does not make sense). 2. No. 3. See 1.
Oct
15
comment Inverse Function Theorem on Zygmund Spaces, is the inverse in the same Zygmund Space?
What I mean is that you should post the same question here and at math.stackexchange simultaneously. This produces unrelated threads and wasted time of the community, see here.
Oct
15
comment Inverse Function Theorem on Zygmund Spaces, is the inverse in the same Zygmund Space?
Please do not cross-post the same question.
Oct
13
comment Is this series well known?
Oops, totally missed that $!$…
Oct
13
comment Is this series well known?
Well, its only loosely related. Your f is almost the integral of $\sum t^{n^2}$…
Oct
13
comment Is this series well known?
Related to (integral of) the theta function $\theta(0,\tau)$, de.wikipedia.org/wiki/Thetafunktion.
Oct
9
comment Proofs without words
I find the underlying argument extremely nice but the picture (especially the animated one) does not really work for me without any words. The animation makes me think that is has some meaning that the yellow dots are visited in a certain order.
Oct
9
comment Why are the angular differences of these random complex polynomial coefficients almost constant?
Yeah sorry, I still had the question mathoverflow.net/questions/182412/… in mind. For roots in the unit square the effect I see is much smaller but still can be seen (still working with double precision floating points). I still tend to blame the random number generators; but this is far from my field and so this suspicion is not backed up…
Oct
8
comment Can one always find sparse solutions to an $\ell^1$-minimization problem?
Question reformulated in terms of the optimality system: $x^*$ is an $\ell^1$-minimal solution if $Ax^*=b$ and there exists $w$ such that $A^T w \in\partial\|x\|_1$. This says: there is no $m$-sparse solution if the range of $A^T$ (which is $m$-dimensional) does not intersect the $m$-dimensional faces of the unit cube. Answers to this question show that for $m\geq n/2$ this can not happen. (Unfortunately, $m$ and $n$ are swapped in the linked question.)
Oct
8
comment Why do roots of polynomials tend to have absolute value close to 1?
This is really strange. My experiments with MATLAB (just with double precision floating points) show strange effects even when I calculate the coefficients of a polynomial which has $N$ roots precisely (up to eps) at the roots of unity when $N$ is as small as 100. I obtain a polynomial with very large coefficients for the middle exponents, and comparably small coefficients close $x^0$ and $x^N$.
Oct
8
comment Why do roots of polynomials tend to have absolute value close to 1?
I notice that this answer is close in spirit to the one by @tros443.
Oct
1
comment ellipsoids have spherical section
Capitalization and punctuation as well as consistent TeX would be helpful.
Sep
29
comment What is the most useful non-existing object of your field?
I use the non-existence of a number that is both positive and negative much more often then the non-existence of a number that is less than and greater than $1$. However, the non-existence of a number that is both positive and negative follows easily: Let $x$ fulfill i) $x<1$ and ii) $x>1$. Then for $y = x-1$ we have by i) that $y<0$ and by ii) that $y>0$ and hence, $y$ has the desired properties. Since $x$ does not exist, $y$ also does not exist either.