bio | website | math.uni-trier.de/~wengenroth |
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location | Universität Trier | |
age | 47 | |
visits | member for | 3 years, 2 months |
seen | yesterday | |
stats | profile views | 1,390 |
I am Professor for Mathematics at the Unversität Trier (Germany)
Apr 6 |
comment |
$\mathcal S(\mathbb R^n) \hat \otimes_\pi \mathcal S(\mathbb R^m) \simeq \mathcal S(\mathbb R^{n+m})$?
Grothendieck called the $\varepsilon$ tensor topology injective. The inductive topology is still finer and even for nuclear spaces it may be different from the injective one. |
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 |
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Is this a sufficient condition for joint normal distribution?
A quick proof is by Fourier transformation. |
Mar 19 |
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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 |
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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 |
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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 |
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Monotonicity of a ratio of conditional expectation operator
By "over a finite product" you probably mean "with values in"? |
Mar 17 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |