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1d
comment Is it possible to have a research career while checking the proof of every theorem that you cite?
Mikhail, does your irony towards Bourbaki mean that you don't approve any activity on systematization of something?
May
1
comment The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
Actually, I don't understand... For which Stein manifold $N$ we have ${\mathcal O}(N)={\mathbb C}[\varepsilon]/\varepsilon^2$?
May
1
revised The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
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May
1
revised The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
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May
1
revised The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
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May
1
comment The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
@nfdc23, is it possible that this is simpler? Let $I_s$ be the ideal of functions in ${\mathcal O}(M)$ vanishing at the point $s\in M$. Actually, I need the following: if a system of functions $f_1,...,f_n\in {\mathcal O}(M)$ form local coordinates in a point $s\in M$ and $f_1(s)=...=f_n(s)=0$, then for any $f\in {\mathcal O}(M)$ the function $f-f(s)-\lambda_1 f_1-...-\lambda_n f_n$ belongs to $(I_s)^2$, where $\lambda_i$ are the partial derivatives of $f$ in the point $s$ along the coordinates $f_i$. Is this true?
May
1
comment The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
OK, thank you!!
May
1
comment The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
Ben, I can't get this paper. Does Rossi prove the homeomorphism of topological spaces or just the equality of sets?
May
1
comment The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
Ah, OK! And what about the tangent space?
May
1
revised The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
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May
1
asked The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
Apr
29
comment Why do we study symplectic geometry?
Questions about applications are very important, and, by the way, they inspire research. It is not good to close them.
Apr
24
comment Attempted Banachification of a space
Will, I am a bit far from this now, this is just my feeling. Can you reformulate your definition in categorical terms (i.e. using linear continuous maps as arrows)?
Apr
24
comment Attempted Banachification of a space
This reminds of the bornologification: books.google.ru/…, or arxiv.org/abs/1110.2013, page 44, example 1.13. I believe, the differences, if any, are not essential.
Apr
7
comment Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@Yemon, independently on how we define the borders, the questions about applications - "why are you doing (/interested in) this?" - are inevitable. Is there a possibility to ask this at MO (or anywhere else)? And do you agree that people who ask this have right to do this?
Apr
6
comment Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@Yemon, in my opinion your doubts about Beurling and the rest are not very serious. There must be more clear rules for decisions like this.
Apr
6
comment Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@IanMorris, I understand you, but there is a difference between some random titles of the articles in GAFA and a possibility to speak with people who have their own opinion on this question.
Apr
6
comment Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@IanMorris, some people don't have access to mathscinet.
Apr
6
revised Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
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Apr
6
answered Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)