arXiv subjects

Atsushi Yamamori

Publications and source records attributed to Atsushi Yamamori.

6 recordsLinked to original sources

arXiv2015

On the linearity of origin-preserving automorphisms of quasi-circular domains in $\mathbb C^n$

A theorem due to Cartan asserts that every origin-preserving automorphism of bounded circular domains with respect to the origin is linear. In the present paper, by employing the theory of Bergman's representative domain, we prove that under certain circumstances Cartan's assertion remains true for quasi-circular domains in $\mathbb C^n$. Our main result is applied to obtain some simple criterions for the case $n=3$ and to prove that Braun-Kaup-Upmeier's theorem remains true for our class of quasi-circular domains.

math.CV↗

arXiv2014

Automorphisms of normal quasi-circular domains

It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using the Bergman mapping, we prove that every origin-preserving automorphism of normal quasi-circular domains in $\mathbb C^2$ is linear.

math.CV↗

arXiv2013

An application of a Diederich-Ohsawa theorem in characterizing some Hartogs domains

Applying a theorem due to Diederich and Ohsawa on weighted Bergman kernels, we characterize some Hartogs domains by their holomorphic automorphisms.

math.CV↗

arXiv2013

The automorphism group of a certain unbounded non-hyperbolic domain

In this paper we determine the automorphism group of the Fock-Bargmann-Hartogs domain $D_{n,m}$ in $\mathbb{C}^n\times\mathbb{C}^m$ which is defined by the inequality ${\|ζ\|}^2<e^{-μ{\|z\|}^2}$.

math.CV↗

arXiv2011

Zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain and the interlacing property

In this paper we consider the zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain $D_{n,m}$. We describe how the existence of zeros of the Bergman kernel depends on the integers $m$ and $n$ with the help of the interlacing property.

math.CV↗

arXiv2010

The Bergman kernel of a certain Hartogs domain and the polylogarithm function

We consider a certain Hartogs domain which is related to the Fock-Bargmann space. We give an explicit formula for the Bergman kernel of the domain in terms of the polylogarithm functions. Moreover we solve the Lu Qi-Keng problem of the domain in some cases.

math.CV↗