bio | website | fernuni-hagen.de/analysis |
---|---|---|
location | Germany | |
age | 36 | |
visits | member for | 2 years, 1 month |
seen | 11 hours ago | |
stats | profile views | 1,263 |
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.
Sep 24 |
comment |
Examples for Markov generators with pure point spectrum
I don't quite understand what you mean by saying that "the only three generators that can arise are the Ornstein-Uhlenbeck, Laguerre and Beta generator". If you consider the Laplacian as a (very) special case of the Ornstein-Uhlenbeck operator, then I agree. In any case, $\Delta$ on $L^2(\Omega)$, $|\Omega|=1$, with Neumann boundary conditions seems to be what you need: It generates a Markov semigroup under very mild regularity assumption on $\partial\Omega$ and its spectrum can be almost arbitrarily complicated, the main constraint being the (dimension dependent) Weyl asyptotic formula. |
Sep 15 |
answered | Results true in a dimension and false for higher dimensions |
Sep 13 |
comment |
Another kind of the positivity of matrices
a matrix fulfilling your notion of positivity is called "positive definite" in linear algebra - that is, in each linear algebra textbook. you can look for answers there. |
Sep 1 |
awarded | Revival |
Aug 29 |
awarded | Yearling |
Jul 2 |
awarded | Curious |
Jun 27 |
revised |
Find multiple non-adjacent paths in a graph
added 121 characters in body |
Jun 27 |
answered | Find multiple non-adjacent paths in a graph |
Jun 16 |
revised |
Continuity with values in L^2
added 1 character in body |
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?
added 10 characters in body |
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. |