bio | website | regularize.wordpress.com |
---|---|---|
location | Braunschweig, Germany | |
age | 36 | |
visits | member for | 4 years, 3 months |
seen | 1 hour ago | |
stats | profile views | 1,788 |
Professor at TU Braunschweig.
Area: Inverse problems, regularization theory, applied functional analysis, mathematical image processing.
Sep 8 |
comment |
“Paradoxes” in $\mathbb{R}^n$
The unit ball is indeed a special convex body. |
Aug 14 |
comment |
Heuristic interpretation of the 'third index' for Besov and Triebel-Lizorkin spaces
That's all well but I don't get a heuristic interpretation of $q$ out of it. Sure, the embeddings are clear but in what sense is $q$ some "fine tuning"? Probably the case $q=\infty$ is interesting: Although the spaces $B^s_{p,\infty}$ are not Sobolev spaces one somehow sees a link to Sobolev regularity. Do you know an example of a function in $B^s_{p,\infty}$ that does not lie in $B^s_{p,p}$? Maybe for $p=2$? |
Aug 14 |
revised |
Heuristic interpretation of the 'third index' for Besov and Triebel-Lizorkin spaces
only fixed umlauts |
Aug 13 |
reviewed | Reject Matching number and chromatic number |
Aug 1 |
comment |
Finding gradient of an optimization
You optimize over a binary variable (which seems to be a binary matrix, right?)? And you want the gradient of the objective with respect to this binary variable $w$? Better relax to $w_{ij}\in[0,1]$ or so. Also: What do you mean by "but for $T(t_i,w)$ is changing in each time step"? |
Jul 30 |
comment |
Spectral multipliers vis-a-vis Differential geometry
Sorry but I don't really get the last motivating questions. Do you say that you would be satisfied by an answer like "Somebody else uses this stuff for something."? But probably this is just my ignorance for the works you point to. |
Jul 26 |
awarded | Nice Answer |
Jul 25 |
comment |
Intuition for Integral Transforms
See also the first chapter of "A guide to distribution theory and Fourier transforms" by Strichartz. |
Jul 25 |
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Decomposition of an integral operator into a composition
I heard that the chebfun2 package for MATLAB can perform some kind of LU decomposition for functions defined on the unit square… |
Jul 25 |
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Intuition for Integral Transforms
(cont) and this is "testing against a characteristic function". Well, that does not fit perfectly to test functions since these are $C^\infty$ but well - the physical world tends to be a bit fuzzy anyway… |
Jul 25 |
comment |
Intuition for Integral Transforms
@TomCopeland I thought that "testing against a function" has a meaning in a physical sense. Consider the quantity you would like to test as some physical quantity, e.g. the temperature distribution in your office or the sugar concentration in your cup of tea. What should you do if you would like to know the value of this at a certain point? [In mathematical terms: do point evaluation.] As a physicist you realize that can't do perform this kind of "test". But what you can do, is to evaluate some kind of "average" (e.g. by taking out some sample of tea with a pipette) (to be continued) |
Jul 24 |
revised |
Both NP-hard but different
corrected spelling, expanded tsp |
Jul 24 |
comment |
Proximal operator of modified L1 matrix norm
There are simple rules for the prox of translations (just do substitution in the minimization problem). For the last case I only expect a simple solution for invertable $M$ (again substitute). |
Jul 24 |
answered | Examples of famous 'workhorse' theorems |
Jul 21 |
comment |
Is this graph of reciprocal power means always convex?
Ok, my believe is destroyed… Another interesting question could be. What are $n$ and $p$ such that the respective function has most negative value in its second derivative? |
Jul 21 |
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Is this graph of reciprocal power means always convex?
Good! It still puzzles me, why the quantity is convex in almost every case. I would still believe if somebody told me that convexity is true for large $n$… |
Jul 21 |
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Is this graph of reciprocal power means always convex?
Some tests with extreme cases seem to indicate that the answer may be negative. The small negative part of the second derivative of the function for $n=3$ and values $p = [0.25\ 0.25\ 0.5]$ (see here) does not look like a numerical artifact. Other values that give suspicious results are tuples with a small number of entries (but more that two) that are close to the uniform distribution. |
Jul 18 |
revised |
Proof correctness problem
Spelled out the acronym CFSG (my google search yielded the correct hit on place five…) |
Jul 16 |
comment |
Metrization of weak convergence of signed measures
Sorry for longer quietness, but may I ask what problems do arise with this metric if the measures are signed? I thought that the constraint $|f(\omega)|\leq 1$ would take care of these. In the metric we use differences of measures anyway so what goes in the norm is generall signed. |
Jul 16 |
reviewed | Approve Sum over growing Young tableaux |