bio  website  math.unitrier.de/~wengenroth 

location  Universität Trier  
age  47  
visits  member for  2 years, 10 months 
seen  1 hour ago  
stats  profile views  1,240 
I am Professor for Mathematics at the Unversität Trier (Germany)
1d

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decomposition of tempered distributions by entire analytic functions
I guess you mean by $g^\vee$ the inverse Fourier transform. Since Fourier transformation is an isomorphism $\mathscr S'\to\mathscr S'$ (with the weak*topology) you need to show that $\sum\limits_{k=1}^K \phi_k \hat f$ converges to $\hat f$ and hence $\langle \sum\limits_{k=1}^K \phi_k \hat f,g \rangle \to \langle \hat f ,g\rangle$ for all $g\in\mathscr S$ (where$\langle f,g \rangle$ denotes the duality between $\mathscr S'$ and $\mathscr S$). For this it would be enough to show $\sum\limits_{k=1}^K \phi_kg \to g$ in $\mathscr S$ and this will depend on bounds for the derivatives of $\phi$. 
1d

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Continuity of a Functional
The question is not clear. What is the domain of $T$? Do you mean by $F^{1}(s)$ the multiplicative inverse $1/F(s)$? 
2d

awarded  Nice Answer 
Nov 20 
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Between compact and locally uniform: What is the name of this convergence?
Very informative answer. A reference would be nice. 
Nov 19 
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Universal maps between topological spaces
@Oblomov Surjectivity is clearly necessary but universality is much stronger (the identity on $\mathbb R$ is surjective but not universal with $f(x)=x+1$). 
Nov 16 
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When is a `1form' with continuous coefficients exact?
Very long second... 
Nov 11 
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Counterexample for closed graph theorem in unmetrizable case
For an infinitedimensional Hilbert space $X$ consider $Y=X$ endowed with the finest locally convex topology and the identical map. On the other hand, if the domain $X$ is ultrabornologial the closed graph theorem holds for socalled webbed spaces introduced by de Wilde. This is a very large class of locally convex spaces which contains all Banach spaces and is stable w.r.t. closed subspaces, separated quotients, and countable products and direct sums. See, e.g., Introduction to Functional Analysis of Meise and Vogt. 
Nov 5 
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Rank of a sequence of covariance matrices
In general, $ZX_i$ are only in $L^1(\Omega,P)$ so that the covariance is not necessarily defined. $Z\in L^\infty$ would be okay. 
Oct 31 
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“Partition” of a smooth function in $\mathbb R^2$
@GHfromMO Formally, you are right. The statement means: For all $f\in C^\infty(\mathbb R^2)$ with $f(0,0)=0$ there are $g_1,g_2 \in C^\infty(\mathbb R^2)$ such that $f(x,y)=g_1(xy,x)+g_2(xy,y)$ for all $(x,y)\in\mathbb R^2$. 
Oct 30 
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Large Deviations: Exponential decay in normed spaces
There is a Banachspace version of Azuma's inequality due to Assaf Naor, theorem 1.5 in [web.math.princeton.edu/~naor/homepage%20files/ARnotes.ps]. There you need however special properties of the norm (modulus of smoothness of power type 2). 
Oct 28 
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Examples of topologies compatible with a given dual pair
The answer to your question depends very much on what you mean by concretely. If the strong topology $\tau$ on $\mathscr E'$ (Schwartz' notation for $C^\infty(\mathbb R)'$) is concrete enough you can restrict it to $\mathscr D= C^\infty_c(\mathbb R)$ to obtain a compatible topology for the dual pair. 
Oct 28 
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Examples of topologies compatible with a given dual pair
You mean $\langle\varphi,f\rangle = \int \varphi(x)f(x)dx$, right? 
Oct 19 
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How to formulate approximation from above?
It would be most natural to assume the continiuty of $X_{j+1} \hookrightarrow X_j$ so that you have a projective limit of Banach spaces. Then $X_\infty=\bigcap_j X_j$ is a Frechet space. 
Oct 18 
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Is every Montel locally convex vector space compactly generated?
The MackeyUlam theorem is discussed in Bonet's and PerezCarreras' book "barrelled locally convex spaces". They write that if a product $\mathbb R^I$ fails to be bornological then the cardinality $d$ of $I$ is "strongly inaccessible". In particular, $a<d$ $\Rightarrow$ $2^a < d$ which is certainly wrong for $c=card(\mathbb R) = 2^{\aleph_0}$. 
Oct 17 
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Is every Montel locally convex vector space compactly generated?
I don't have any references at hand, but I think that products of "moderate cardinality" are bornological, in particular, I believe that $\mathbb R^{\mathbb R}$ is bornological even without assuming the continuum hypothesis. 
Oct 16 
answered  Is every Montel locally convex vector space compactly generated? 
Oct 16 
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Is every Montel locally convex vector space compactly generated?
A counterexample to the BanachDieudonne theorem for nonmetrizable spaces was first given by Komura [link.springer.com/article/10.1007%2FBF01361183] 
Oct 16 
accepted  Consistent price index 
Oct 15 
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Is every Montel locally convex vector space compactly generated?
KrieglMichor really mean by $kX$ the finest topology (not necessarily locally convex) making all inclusions of compact subsets continuous. The proof uses the the BanachDieudonne theorem for which metrizability is quite essential. 
Oct 14 
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Consistent price index
Excellent. Although it looks slightly simpler than Bjorn KjosHannssen's solution it is essentially the same. Unfortunately, I can's share the bounty and Bjorn was a little bit faster. 