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Apr
16
comment Heat kernel and Wiener measure
Ok, now I understand what you meant! As you said, this argument is still lacking of rigour. Can it be that the probability measure is choosen in such a way, that the set A doesn't have measure zero? At least there should be a rigorous justification, since these statements are used by mathematicians to achieve more fancy results
Apr
15
comment Heat kernel and Wiener measure
First of all, thank you for your help! I don't know how to use Bayes formula in this situation. Can you tell me how the probability measures are linked with each other?
Apr
14
asked Heat kernel and Wiener measure
Jan
4
comment What is the right initial domain for the Dirichlet-Laplacian on a bounded domain?
Ok thank you. So I assume that the Friedrichs extension of $-\Delta:C^{\infty}_0 (\Omega)\subset L^2(\Omega)\rightarrow L^2(\Omega)$ is equal to the other one. Is that right?
Jan
4
asked What is the right initial domain for the Dirichlet-Laplacian on a bounded domain?
Jul
27
awarded  Disciplined
Jul
25
awarded  Yearling
Jul
24
awarded  Commentator
Jun
26
accepted Eigenfunctions of Schrödinger Operators on the boundary
Jun
22
comment Eigenfunctions of Schrödinger Operators on the boundary
What do you mean by "test functions". Smooth functions with compact support (in our case this would mean all smooth functions)?
Jun
22
comment Eigenfunctions of Schrödinger Operators on the boundary
Thank you for the comment. Actually I wasn't looking for a physical reason (there is no ambient space in my situation).
Jun
20
asked Eigenfunctions of Schrödinger Operators on the boundary
May
20
comment The first eigenvalue of the Schrödinger operator is simple.
You are using the elliptic regularity. What happens if the potenital V is not smooth but just bounded? I think the eigenfunctions will not be smooth anymore. Does the statement remeins true for this case or are there counterexamples?
May
20
revised The first eigenvalue of the Schrödinger operator is simple.
added 426 characters in body
May
20
asked The first eigenvalue of the Schrödinger operator is simple.
May
20
accepted regularity of eigenfunctions of Schrödinger Operator
May
20
asked regularity of eigenfunctions of Schrödinger Operator
May
18
accepted Resolvent of Laplacian
Apr
4
asked Resolvent of Laplacian
Mar
15
awarded  Scholar