1,201 reputation
317
bio website fernuni-hagen.de/analysis
location Germany
age 36
visits member for 2 years, 3 months
seen 3 hours ago

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.


Nov
13
awarded  Popular Question
Nov
5
asked significance of the Fučík spectrum
Oct
23
comment Disruptive innovations in mathematical notations
notation for matrices! which made matrix multiplication possible in the very first place.
Oct
20
accepted eigenvalue estimate of the adjacency matrix
Oct
13
comment eigenvalue estimate of the adjacency matrix
On the Spectral Radius of (0,1)-Matrices, LAA 1985
Oct
10
comment eigenvalue estimate of the adjacency matrix
thanks a lot! by now i have found a further upper estimate in a paper by brualdi and hoffman, but i am still quite surprised that so little is known about the adjacency matrix - as opposite to the laplacian, in particular.
Oct
9
comment eigenvalue estimate of the adjacency matrix
$\lambda_\min $
Oct
9
comment eigenvalue estimate of the adjacency matrix
plus, $A^T=A$ anyway :)
Oct
9
asked eigenvalue estimate of the adjacency matrix
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 $sp>{\rm dim } M$?