Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bergman kernel and projection on the unbounded worm domain   In this paper we study the Bergman kernel and projection on the unbounded
worm domain $$ \mathcal{W}_\infty = \big\{(z_1,z_2)\in\mathbb{C}^2 :
\big|z_1-e^{i\log|z_2|^2}\big|^2<1, z_2\neq0\big\}. $$ We first show that the
Bergman space of $\mathcal{W}_\infty$ is infinite dimensional. Then we study
Bergman kernel $K$ and Bergman projection $\mathcal{P}$ for
$\mathcal{W}_\infty$. We prove that $K(z,w)$ extends holomorphically in $z$
(and antiholomorphically in $w$) near each point of the boundary except for a
specific subset that we study in detail. By means of an appropriate asymptotic
expansion for $K$, we prove that the Bergman projection $\mathcal{P}:W^s\not\to
W^s$ if $s>0$ and $\mathcal{P}:L^p\not\to L^p$ if $p\neq2$, where $W^s$ denotes
the classic Sobolev space, and $L^p$ the Lebesgue space, respectively, on
$\mathcal{W}_\infty$.

21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an