bio | website | math.uni-trier.de/~wengenroth |
---|---|---|
location | Universität Trier | |
age | 46 | |
visits | member for | 2 years, 2 months |
seen | 4 hours ago | |
stats | profile views | 895 |
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 |