3,184 reputation
1348
bio website regularize.wordpress.com
location Braunschweig, Germany
age 36
visits member for 4 years, 2 months
seen 16 hours ago

Professor at TU Braunschweig.

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


Nov
4
comment Polynomials with prescribed points to match prescribed bounds
Oh, there is a simpler argument: Since there are piecewise monotone interpolating polynomials we can use them directly to interpolate the $x^+$ and $x^-$ (and possibly adding zero interpolation points inbetween).
Nov
4
comment Polynomials with prescribed points to match prescribed bounds
Such a polynomial always exists: Take a Chebycheff polynomial $P$ of degree high enough (such that is attains the values 1 and -1 in the right order at point $t_i$. Then choose a monotone polynomial $Q$ which maps the points $t_i$ to the prescribed $x_i$ and take $P\circ Q$. Such monotone polynomial interpolants exit by a theorem of Young (ams.org/mathscinet-getitem?mr=0212455).
Nov
3
comment Polynomials with prescribed points to match prescribed bounds
That is pretty clear. I am willing to add more assumptions and not hoping for a very clean answer.
Nov
3
asked Polynomials with prescribed points to match prescribed bounds
Oct
27
comment Find vector in R^n which is orthogonal to given (n-1) vectors v_i under condition v_i are orthonormal.
Look at this en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process
Oct
23
comment Low degree polynomial approximation for the entropy function
It would also be good to know what "good" means in your context. Uniform approximation? Mean squared? Or even Kullback-Leibler?
Oct
17
comment What is the maximum diameter of $N$ steps of a random walk?
Thanks! Probably I should note that also the expected value would be helpful.
Oct
14
comment What is the maximum diameter of $N$ steps of a random walk?
@cardinal: Bounds would also be helpful as well as asymptotic results. I briefly went over the papers you linked - as I understood thay all rely in some way on the ordering of the reals and hence, generalization seems not to be straightforward...
Oct
14
comment What is the maximum diameter of $N$ steps of a random walk?
Thanks so far for the comments and references! I'll check them out. @Igor: Is this also called Brownian motion if it is time discrete? Would it be right to say that the time discrete model is a sampled continuous Brownian motion? Sorry for my ignorance on this topic...
Oct
13
asked What is the maximum diameter of $N$ steps of a random walk?
Oct
12
comment Best Poincare constants on the surface of a ball
Are there any such maps $\xi$ in the case of $\mathbb{R}^2$ which are in $H^1$?
Oct
7
comment Fast root finding for strictly decreasing function
How fast? Is the derivative available? What is wrong with bisection?
Sep
30
awarded  Yearling
Sep
26
comment One-line proof of the Euler's reflection formula
Could a down-to-earth proof have one line?
Sep
20
comment Do you know this form of an uncertainty principle?
I got a little bit confused with all these different inequalities around (many of them called Caffarelli-Kohn-Nirenberg) but now I see. That's an interesting relation though. The Heisenberg uncertainty is also included? ($\gamma=\alpha=0$, $\beta=−1$, $a=1/2$)
Sep
20
comment Do you know this form of an uncertainty principle?
Wow, there are lot of constants involved. As far as I've seen, it seems that the case $\gamma=0$, $a=1$ and $\alpha=-1$ is not included?
Sep
20
asked Do you know this form of an uncertainty principle?
Sep
19
comment Decomposing max-convolution of sum of functions ?
Sorry, I do not get several points: What are $x$, $y$, $dx$ and $dy$? What are the $d_i$'s? What do you mean by "random" matrices (especially in the light that they seem to depend on $x$ and $y$)?
Sep
12
comment Unique limits of sequences plus what implies Hausdorff?
Thanks! Especially the topospaces.subwiki.org is pretty cool...
Sep
7
revised When does symmetry in an optimization problem imply that all variables are equal at optimality?
Corrected wording