3,463 reputation
1751
bio website regularize.wordpress.com
location Braunschweig, Germany
age 36
visits member for 4 years, 7 months
seen 3 hours ago

Professor at TU Braunschweig.

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


Dec
21
comment Open problems in compressed sensing
One thing is that it makes a huge difference if one answers this question as a mathematician or as an engineer. Well, of course this is site for mathematics but the idea of compressed sensing is really a practical one: get information about a high dimensional object that lives in lower dimensional but nonlinear subspace from few measurements. The meaning of all ingredients is debatable here and varies a lot from problem to problem. Hence one open problem is to find the right mathematical formulation of the problem...
Dec
19
comment Image of (right) inverse trace map $\xi\colon H^{\frac 12}(\partial\Omega) \to H^1(\Omega)$ dense in $H^1(\Omega)$?
Ok, right - I thought that I had a basic misconception about the problem…
Dec
19
comment journal to submit mathematic books' review
The German "Mathematische Semesterberichte" publishes such reviews (probably only in German).
Dec
19
reviewed Close How to construct a graph with arbitrarily large girth and large chromatic number?
Dec
19
reviewed Leave Open Image of (right) inverse trace map $\xi\colon H^{\frac 12}(\partial\Omega) \to H^1(\Omega)$ dense in $H^1(\Omega)$?
Dec
19
comment Image of (right) inverse trace map $\xi\colon H^{\frac 12}(\partial\Omega) \to H^1(\Omega)$ dense in $H^1(\Omega)$?
Isn't solving the respective Dirichlet problem saying that the image contains $H^{3/2}$?
Dec
16
reviewed Close Alexander duality theorem
Dec
11
revised What is an extragradient method?
corrected spelling
Dec
10
answered Galerkin Projection on Integral Operators
Dec
10
answered What is an extragradient method?
Dec
7
comment Banach space of discontinuous functions(Killing continuous functions)
"Appropriate quotient space" Do you have an idea how this space looks like (or how the space which you divide by)? I guess the quotient contains all characteristic functions of all points and then it wouldn't be separable in the first norm. The second norm looks pretty weired to me…
Dec
4
comment $Ax=b$ in a function space
I am not sure what you are after. Do you want to show that the solution depends continuously on the matrix? Are you especially interested in the case where $A$ gets singular?
Nov
27
awarded  Notable Question
Nov
25
accepted Geometric measures different from Hausdorff
Nov
25
comment Reference for a strong intermediate value theorem for measures
Actually, your statement is not strictly stronger than the result the OP is asking for since he wants the sets $S_t$ to be nested.
Nov
20
reviewed Leave Open “Almost” zeta function
Nov
19
comment Removing constraints in convex optimization
Well, ehm, actually I don't see it either… Adapted my answer which is only a "partial answer" now…
Nov
19
revised Removing constraints in convex optimization
Extended and corrected
Nov
19
comment What's the idea behind various equivalent norms on Besov spaces $B^{s}_{p,q}$?
Another book that is quite detailed is Runst and Sickel's Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations. However, I guess for the equivalence of the norms they refer to Triebel…
Nov
19
comment Geometric measures different from Hausdorff
Thanks a lot for the answer, especially for pointin to Frostman's lemma, densities and the example where $H^m(A)>0$ and $G_m(A) = 0$. This is exactly in the direction I was hoping. If you had additonally some concrete examples where Hausdorff, Dyadic and Spherical Measure differ I would accept and cash the bounty right away!