2,795 reputation
931
bio website math.uni-trier.de/~wengenroth
location Universität Trier
age 47
visits member for 3 years, 1 month
seen Mar 26 at 14:36
I am Professor for Mathematics at the Unversität Trier (Germany)

Mar
23
awarded  Necromancer
Mar
23
revised Is Schauder's Conjecture Resolved?
arXiv link added
Mar
23
answered Is Schauder's Conjecture Resolved?
Mar
20
revised Is a Fréchet Montel space distinguished?
corrected spelling
Mar
20
comment Is this a sufficient condition for joint normal distribution?
A quick proof is by Fourier transformation.
Mar
19
comment Topological properties of space of Radon measures
Did you try something with the Jordan-Hahn decomposition? For real-valued measures you would have a continuous surjection $M_+\times M_+ \to M$, $(\nu,\mu)\mapsto \nu-\mu$.
Mar
19
comment Topological properties of space of Radon measures
Why is the subset of positive measures polish? I believe that the set of probability measures is polish.
Mar
19
answered Is a Fréchet Montel space distinguished?
Mar
19
comment Is this a sufficient condition for joint normal distribution?
That $C$ is positve semi definite follows from the assumption. One has to allow variance $0$ for a normal distribution (which is then a Dirac measure).
Mar
17
comment Monotonicity of a ratio of conditional expectation operator
By "over a finite product" you probably mean "with values in"?
Mar
17
comment Is it true that for each bounded continuous function we can find a set of analytic functions to uniformly converge it?
Don't you need uniformly continuous functions to get uniform convergence?
Mar
6
comment Abstract connectedness
Two connected components are either equal or disjoint, hence they form a partition of the underlying set. One could thus consider the full subcategory of pairs $(X,C_X)$ where $C_X$ is a partition of $X$. Given a partition $C_X$ ox $X$ the system of all unions $\bigcup M$ with $M\subseteq C_X$ is then a topology so that the elements of $C_X$ are the connected components.
Mar
2
comment Inductive/Projective Limits of Topological Algebras
Your first example of $C^k$-functions with compact support isn't a Frechet space (the intersection of the classes of Frechet and LB-spaces is the class of Banach spaces).
Feb
19
comment Consistency Conditions of the Kolmogorov Extension Theorem
No, $\pi_I^J$ is THE canonical projection, namely the restriction $\mathbb R^I \ni f \mapsto f|_J$.
Feb
19
comment Consistency Conditions of the Kolmogorov Extension Theorem
This is a matter of notation. It would be much better to state the condition without an artificial ordering of the finite sets: For all finite sets $I\subseteq T$ there are given probability measures $\nu_I$ on $\mathbb R^I$ such that the image of $\nu_I$ under the projection $\pi_I^J: \mathbb R^I\to \mathbb R^J$ is $\nu_J$ for every $J\subseteq I$.
Feb
18
comment Topological tensor products of spaces of holomorphic functions of slow growth
Such questions have been investigated e.g. by K.-D. Bierstedt and R. Meise in the early 1970s. Your case might be contained in Meise's article Räume holomorpher Vektorfunktionen mit Wachstumsbedingungen und topologische Tensorprodukte (Math. Ann. 199 (1972), 293–312).
Feb
18
comment A Characterization of Closed Ideals in $C^{\infty}(\mathbb{R}^n)$
The standard references to this subject are Malgrange's book Ideals of differentiable functions and the one of Tougeron Ideaux de fonctions differentiables. In higher dimensions things become quite complicated: The function $f(x,y)=y^2 - \exp(-1/x^2)$ generates a closed ideal in $\mathscr E(\mathbb R^2)=C^\infty(\mathbb R^2)$ (i.e., $\lbrace fg: g\in\mathscr E(\mathbb R^2)\rbrace$ is closed) whereas $g(x,y)=y^2 + \exp(-1/x^2)$ does not (this is example 4.8 in Tougeron's book).
Feb
4
revised Example of noncomplete quotient of complete lcs mod closed subspace
deleted 2 characters in body
Feb
4
answered Example of noncomplete quotient of complete lcs mod closed subspace
Feb
3
revised Is $ {C_{c}}(G) $ a meager subset of $ {L^{2}}(G) $ for a second-countable locally compact Hausdorff group $ G $?
index of X_k changed to X_K