bio | website | fernuni-hagen.de/analysis |
---|---|---|
location | Germany | |
age | 36 | |
visits | member for | 2 years, 3 months |
seen | 3 hours ago | |
stats | profile views | 1,309 |
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 $sp>{\rm dim } M$? |