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Oct
15 |
accepted | Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$? |
Oct
15 |
comment |
Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$?
I think there is a problem with your approach, since the integral $\int_d^{d+1}\frac{1}{(\cosh(s)-\cosh(d))^{3/2}} ds$ do not converge, so that it is not justified to change integral and derivative. |
Oct
14 |
comment |
Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$?
Yes, your idea is nice! But it seems not clear to me how to compute the derivative $\partial_d k(r,d)$ or to estimate it. |
Oct
14 |
revised |
Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$?
added 129 characters in body |
Oct
14 |
revised |
Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$?
added 71 characters in body; edited title |
Oct
13 |
asked | Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$? |
Feb
17 |
accepted | Fundamental solution to the heat equation with zero boundary values |
Feb
17 |
asked | Fundamental solution to the heat equation with zero boundary values |
Jan
27 |
accepted | holomorphic continuation |
Jan
26 |
asked | holomorphic continuation |
Dec
1 |
accepted | Formula for the Perimeter of a spherical triangle? |
Dec
1 |
comment |
Formula for the Perimeter of a spherical triangle?
Thanks for your help! This is a nice formula. In my understanding this formula doesn't work for triangles with any of its lengths $\ell_i>\pi$. Do you agree or am I missing something? |
Dec
1 |
asked | Formula for the Perimeter of a spherical triangle? |
Sep
7 |
comment |
Boundary regularity of Dirichlet Eigenfunction on bounded domains
Thank you very much! @Christian: Why should there be a problem? Do you have an exceptional situation in mind? |
Sep
6 |
asked | Boundary regularity of Dirichlet Eigenfunction on bounded domains |
Aug
7 |
comment |
construction of heat kernels for non-compact manifolds with boundary
Did you find an answer to your question in meanwhile? I'm wondering, if one can construct the dirichlet heat kernel for unbounded domains with boundary this way (e.g. unbounded domains in euclidean space). |
Aug
4 |
comment |
Existence of the Dirichlet heat kernel for arbitrary open subsets?
@Chrisitan: Thank you! What do you mean by $e^{t\Delta}$? In my experience this symbol occurs in two situations. First in the context of 'continuous functional calculus'. And second in the theory of 'strongly continuous semigroups'. Maybe all of them correspond to the same operator, but I'm not sure. I would be very glad, if you can explain it to me? |
Aug
3 |
accepted | How to evaluate the wiener measure of sets? |
Aug
3 |
asked | Existence of the Dirichlet heat kernel for arbitrary open subsets? |
Jul
14 |
comment |
How to evaluate the wiener measure of sets?
Thank you very much for your help! I have to think some time about your approach and probably will tell you whether it helps. |