# Tagged Questions

Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.

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### Decay estimate of an inverse Fourier transform in R^n [closed]

Is there decay estimate that $\int_{\mathbb R^n}\frac{1}{\xi^2+1} e^{ix\cdot\xi}$ decays like $log|x|$ when $n=2$ and $|x|^{1-n}$ when $n\geq 3$? I don't know how to estimate this non absolute ...
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### problem related to conformal map of doubly connected region [closed]

Is the explicit result known? Product[(1 - Cos[x]/Cosh[n*h]), {n, 1, Infinity}]
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### Smooth quotients of algebraic spaces that are varieties away from codimension $\ge 2$ subset

This is a question about when a smooth complex algebraic space that is very close to being an algebraic variety is actually an algebraic variety. General question: Let $X$ be a smooth separated ...
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### Intersection of two curves is not Cohen Macaulay

Let be $R=\mathbb{C} \lbrace x,y,z \rbrace$ the formal series ring and let $f_{1},f_{2},f_{3} \in R$ be nonzero elements of $R$. (a) Consider the varieties $M:=V(f_{1},f_{2})$ and $N:=V(f_{2},f_{3})$ ...
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### Is an bijective analytic map bi-analytic?

Suppose that $E$ and $F$ are complex Banach spaces and $U\subset E$ and $V\subset F$ are open subses. $f\colon U\to V$ is analytic $f\colon U\to V$ is bijective Is $f$ bi-analytic? (i.e. is its ...
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### Neighborhoods with proper multiplication

The following question was originally asked here, by C. Dubussy: http://math.stackexchange.com/questions/1802111/neighbourhoods-with-proper-multiplication Assume we have two closed subsets $F$ and $G$...
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### Does cutting off the taylor expansion of e^x always give an irreducible polynomial? [duplicate]

I am talking of the polynomials: $P_n(x)$ = $1+x..+x^n/n!$ I've tested this for the first 10 values and it seems so. I know this might be random but I've got a hunch that there's something deeper ...
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### Can an algebraic function be zero both at $z=0$ and at its leading singularity?

Apologies for asking possibly strange questions, but I am just a poor computer scientist trying to understand a mathematical paper on singularity analysis of algebraic functions that is apparently not ...
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### Is polynomial convexity a topological invariant?

Is the property of being polynomially convex a topological invariant? In other words, let $M$ and $N$ be two homeomorphic, compact subsets of $n$-dimensional complex Euclidean space, and assume in ...
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### Functions of form $f(z)/f(z^*)$

I am doing my research in mathematical physics, and in the process I am getting functions of complex variable $z$ of form $F(z) = \frac{f(z)}{f(z^*)}$ In my case $f$ doesn't have any interesting ...
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### Complex Stone-Weierstrass Type problem

I have come across this problem which resembles complex Stone-Weierstrass theorem except for a problem that the conjugate of the functions are not necessarily in the sub algebra. Suppose $\Omega$ is ...
Let $A$ be a Fréchet algebra over ${\mathbb C}$, and let us call the spectrum ${\tt Spec}[A]$ of $A$ the set of all characters, i.e. continuous multiplicative linear functionals $s:A\to{\mathbb C}$, ...