3,174 reputation
1348
bio website regularize.wordpress.com
location Braunschweig, Germany
age 36
visits member for 4 years, 2 months
seen 4 hours ago

Professor at TU Braunschweig.

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


9h
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…
10h
comment journal to submit mathematic books' review
The German "Mathematische Semesterberichte" publishes such reviews (probably only in German).
14h
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
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
25
comment Continuous versions of tensors/ Tensors with infinite indices?
A situation where this works pretty straightforward is the case of functionals on $L^2$ (also on $L^p$ with $1<p<\infty$). There, the functionals are identified with functions, e.g. $(L^2)'=L^2$ and the tensor product of $L^2$ with itself is simple enough (en.wikipedia.org/wiki/Tensor_product_of_Hilbert_spaces).
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
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
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!
Nov
14
comment Noncommutative version of Littlewood's First Principle
While the title sounds interesting to me, I have to admit that I don't have any idea what this "noncommutative setting" you are talking about may be, let alone what an analog of Littlewood's principle may be.
Nov
13
comment Does the boundary of a convex body contain a regular planar pentagon?
Does a convex body need to have nonempty other interior? Otherwise the answer is no.
Nov
9
comment Area of the minimal surface of a non-planar quadrilateral in 3d
Regarding your other comment: I thought 'minimal surface' would mean 'surface of minimal area' but probably there are some local minima (whatever this means in this context)?
Nov
9
comment Area of the minimal surface of a non-planar quadrilateral in 3d
A formula in elliptic functions or another non-elementary integral would be OK. In the end I would be happy with a simple numerical method to calculate the value.
Nov
3
comment Maximum of a mollified/convolution function
Questions like this have been treated in the concept of "scale space methods" in mathematical image processing about 15 or 20 years ago where one was interested in the question: How many local minima and maxima survive after convolution and can new local minima or maxima be created? Unfortunately I forgot about the exact references but one result was along the lines: If you take a scale kernel $\phi_t(x) = 1/t\phi(x/t)$ and require that the number of local maxima and minima of $\phi_t\ast f$ is decaying with $t$, and some more hypotheses, then $\phi$ is a Gaussian…
Oct
30
comment numerical solver for stochastic optimal control problems
I think this is better suited for computational science over at scicomp.stackexchange.com.
Oct
29
comment Central-Slice-Theorem Analogue for Wavelet Transforms?
Why do you think that such analog should exist? The 2D Fourier transform and the 2D wavelet transform are not really similar things. You are aware of the fact that the wavelet transform results in a function that lives on a different set, right? Meanwhile, you may be interested in the ridgelet transform which combines the Radon and the wavelet transform.
Oct
27
comment Anti-bidiagonal matrix with main anti-diagonal {1,2,3,…} and first sub-anti-diagonal {-1,-2,-3,…} has eigenvalues lambda={1,-2,3,-4,…}
Have you looked at the eigenvectors?
Oct
23
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.
Oct
21
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).