bio | website | uni-ulm.de/en/mawi/analysis/… |
---|---|---|
location | Germany | |
age | 35 | |
visits | member for | 1 year, 11 months |
seen | yesterday | |
stats | profile views | 1,229 |
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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