1,113 reputation
215
bio website uni-ulm.de/en/mawi/analysis/…
location Germany
age 35
visits member for 1 year, 11 months
seen yesterday

I work on evolution equations, sometimes on their applications too. I am interested in PDEs and functional analysis. I am fond of algebraic graph theory.


Jul
2
awarded  Curious
Jun
27
revised Find multiple non-adjacent paths in a graph
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Jun
27
answered Find multiple non-adjacent paths in a graph
Jun
16
revised Continuity with values in L^2
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Jun
10
comment $H^s(\mathbb T)$ is a Banach algebra for $s>1/2$
But 7.57 is an imbedding result for Sobolev spaces on domains of $\mathbb R^n$! How does this implies the claimed property? I have checked a bit in the literature: It seems that Thm. 3.5 in Sobolev spaces on Riemannian manifolds by E. Hebey settles my question.
Jun
7
comment $H^s(\mathbb T)$ is a Banach algebra for $s>1/2$
Can you provide a reference for your last assertion? Does one have that $W^{s,p}(M)\hookrightarrow L^\infty(M)$ if $sp>{\rm dim } M$?
Jun
5
accepted doubly-stochastic isomorphisms of graphs
Jun
3
comment How to model a time-discrete heat equation on a graph?
I see. But then why won't you use a time-continuous model? Then the solution would be given by the semigroup generated by the Laplacian (with negative sign if you want to converge towards equilibrium).
Jun
2
revised How to model a time-discrete heat equation on a graph?
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Jun
2
answered How to model a time-discrete heat equation on a graph?
May
31
comment Heat equation with graph laplacian
is there a reason for deleting the very same question (which had already received some comments) and repost it here?
May
29
comment Time-inhomogeneous Markov Chains
I would like to add that in the field of differential equations on Banach spaces (which contain time continuous Markov chains as special cases) transition matrices that can vary over time become time-dependent operators. There is a well-developed (if not very elementary) theory for this kind of problems, which starts by replacing $C_0$-semigroups by objects called "evolution families". And yes, much is known the long time behavior of this kind of problems: see e.g. www.math.kit.edu/iana3/~schnaubelt/media/survey1.pdf
May
21
comment Should a theorem be numbered by where it is first stated or where it is proven?
I completely agree with Trevor Wilson. You give a theorem a number for the sake of later reference, but if a later reference is already easy and possible, why bother?
May
20
awarded  Nice Question
May
20
comment doubly-stochastic isomorphisms of graphs
thanks, now i understand.
May
20
comment doubly-stochastic isomorphisms of graphs
sorry, perhaps i am missing something, but since the petersen graph is cubic, how can $\frac{1}{6}A$ be doubly stochastic? shouldn't it be renormalized to $\frac{1}{3}A$?
May
20
comment doubly-stochastic isomorphisms of graphs
I have tried all graphs on 4 nodes and all of them are compact :)
May
18
comment Mathematical equivalent to ladder operators?
It may be a stupid question, but I don't understand why your operator has discrete spectrum. What happens if $V\equiv 0$? The spectrum of the second derivative on $L^2(I)$ is absolutely continuous if $I=\mathbb R$. Or are you assuming $I$ to be bounded?
May
15
comment Solving PDE via Cellular Automata
There are quite a few works in theoretical computer science (google for Belkin, Hein, von Luxburg, to begin with) that state results like: Take a manifold and some (randomly chosen) sample points on them. Define in this way a discrete(=graph) Laplacian. Then the discrete Laplacian will converge towards the Laplace-Beltrami operator on the original manifold as the sample points exhaust the manifold.
May
14
revised doubly-stochastic isomorphisms of graphs
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