In this paper we determine the automorphism group of the Fock-Bargmann-Hartogs domain Dn,m in C n ×C m which is defined by the inequality ζ 2 < e −µ z 2 .

In this paper we consider the zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain {(z, ζ) ∈ C n × C m ; ||ζ|| 2 < e −µ||z|| 2 } where µ > 0. 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.2000 Mathematics Subject Classification. 32A25.

No abstract

Abstract. 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 C 2 is linear.

No abstract