All Questions
3,560 questions
1
vote
0
answers
278
views
Localization in analytic geometry
Let $X$ be a Stein complex analytic space, and let $Z$ be a closed complex analytic subspace. Set $U=X-Z$.
I was wandering if there is any relationship between $A_1:=\mathcal{O}_X(U)$
and the ...
- 23.4k
2
votes
0
answers
139
views
Question on Bergman minimal domains
Let $D \subseteq \mathbb{C}^n$ be a bounded domain and let $t \in D$. We say that $D$ is a minimal domain with center $t$ if for each biholomorphism $F:D \to D' \subseteq \mathbb{C}^n$ such that $JF(t)...
- 1,169
1
vote
0
answers
109
views
Bounding a q-expansion on a bounded open subset of the complex upper-half plane
Let $f:\mathbf{H}\to \mathbf{C}$ be a holomorphic function on the complex upper-half plane and let $q:\tau\mapsto \exp(\pi i \tau)$ be the nome on $\mathbf{H}$. Suppose that there are integers $a_j$ ...
- 11
0
votes
1
answer
198
views
An integral arising in statistics(2)
The integral I am interested in is:
$$t(x)=\int_{-K}^{K}\frac{\exp(ixy)}{1+y^{2q}}dy$$
$K<\infty$, q natural number
For q=1 one can use contour integration.
So for K>1 we have :
$$\pi/2-\...
- 267
2
votes
0
answers
153
views
Holomorphic automorphism of strictly psudo-convex domain smooth on boundary
I am wondering if anything is known about this. I couldn't find anything in the literature.
In '74 C. Fefferman published a solution to the following problem.
Let $\sigma:D\rightarrow D$ be an ...
- 496
1
vote
0
answers
129
views
Relation between different spatial derivatives of a random field (related to complex integral and/or bessel function)
2 random fields $b$ and $c$ are derived from random field $a$ by
$b=\nabla^2a\equiv(\partial_{xx}+\partial_{yy})a $
and
$c \equiv c_1+i c_2 = (\partial_{xx}-\partial_{yy}+2i \partial_{xy}) a$.
(...
- 111
6
votes
0
answers
161
views
Multiplicity of zero (higher dimensional analog)
Consider a sistem of n holomorphic equations with n unknowns in a neighborhood of zero. Suppose that a solution in a neighborhood of 0 is a k-dimensional manifold.
I want to associate to it some ...
- 61
1
vote
0
answers
113
views
Unbounded Convex domain
Take an unbounded convex domain in C^n, with n>1. Suppose that it is Kobayashi hyperbolic. Is it true that it is biholomorphic to a BOUNDED convex domain? For n=1 it is true due to the Riemann mapping ...
- 11
3
votes
0
answers
131
views
Slicing the fibres of a meromorphic function with the zero set of a section of an ample line bundle
I'm going through a proof of a vanishing theorem by Sommese ($H^{p,q}(X,L) = 0$ for $p+q > n+k$ if $L$ is $k$-ample) and have hit the following brick wall:
I've got a complex projective manifold $...
- 4,343
0
votes
0
answers
36
views
Derivate involving Bessel function of second type
Let.
$$f := (x, y) \mapsto \text{BesselK}(1, c \cdot (a - b \cdot (x + y))) \cdot \exp(c \cdot b \cdot (y - x))$$
Is there a close formula for this $$\frac{\partial^{m+n}}{\partial y^m \partial x^n} f(...
- 109