2,027 reputation
522
bio website math.uni-trier.de/~wengenroth
location Universität Trier
age 46
visits member for 2 years, 2 months
seen 4 hours ago
I am Professor for Mathematics at the Unversität Trier (Germany)

Apr
10
comment question about uniform continuity under Skorokhod Metric
You are probably right but $y_n\to 0$ is claimed in Billigsley's book (the case $\alpha=0$ there).
Apr
9
comment question about uniform continuity under Skorokhod Metric
Neither is the second continuous: $y_n=I_{[0,1/n)} \to 0$ but $S(y_n)=1$.
Apr
9
comment question about uniform continuity under Skorokhod Metric
The first map $\pi$ is not even continuous: The indicator functions $x_n=I_{[0,1/2+1/n)}$ converge to $x=I_{[0,1/2)}$ (see Billingsley's book before example 12.1) but $\pi(x_n)=1$ does not converge to $\pi(x)=0$.
Apr
4
revised A version of von Neumann inequality
Added the functional-analysis tag
Apr
3
comment Final topology of surjective linear map on Banach space
I agree that this is not research level. Is there any need to close when it is answered and the answer is accepted?
Apr
3
answered Final topology of surjective linear map on Banach space
Mar
25
comment Topology on the set of analytic functions
The universal property of $E$ follows from Schwartz' $\varepsilon$-product (which in many cases coincides with the completed injective tensor product): $H(U,X) = H(U) \varepsilon X = L(H(U)'_{co}, X)$ where the last equality is the definition and $F'_{co}$ is the dual of the locally convex space $F$ endowed with uniform convergence on all absolutely convex compact sets. Since $H(U)$ is a Montel space, in our case this is the same as the strong dual of $H(U)$.
Mar
24
comment A linear consequence of the Michael selection theorem
There are always a continuous selection and linear selection (playing with Hamel bases) but of course not always a continuous linear one.
Mar
17
answered Sum of two independent random variables
Mar
10
comment Epi-convergence to indicator function
Since you did not get answers, it might be a good idea to add the definition of epi-convergence.
Mar
7
answered Determine joint distribution from projections
Mar
6
comment Simultaneous Orthogonal basis for $L^2(\mathbb{R}^n)$ and $H^1(\mathbb{R}^n)$
There is also an abstract argument for a common basis (for bounded $U$): If $i:H\to K$ is a compact inclusion between Hilbert spaces with dense range the Schmidt representation of $i$ gives a common orthogonal basis.
Mar
6
answered Spectral theorem for unbounded self-adjoint operators on REAL Hilbert spaces
Feb
27
revised Tietze's extension theorem for compact subspaces
added 428 characters in body
Feb
27
accepted Tietze's extension theorem for compact subspaces
Feb
26
comment Tietze's extension theorem for compact subspaces
@alpha: of course, I meant surjective. The countable case is clear. In particular, the space can't be $\sigma$-compact.
Feb
26
revised Tietze's extension theorem for compact subspaces
little correction
Feb
26
comment Dimension of $L(E,F)$
As you know, for $E=F=k$ the space $L(E,F)$ is one-dimensional. In general, if $B$ and $C$ are bases of $E$ and $F$ I think that you have quite naturally $L(E,F)\cong F^B \cong \lbrace \phi:B\times C\to k:$ for all $b\in B$ only finitely many $c\in C$ satisfy $\phi(b,c) \neq 0\rbrace$. My feeling is that the dimension of this space should only depend on $B$ and $C$.
Feb
26
asked Tietze's extension theorem for compact subspaces
Feb
26
revised Method to compute fundamental solutions which are distributions
Added the functional-analysis tag