We give an example of a bounded, pseudoconvex, circular domain in Cn for any n ≥ 3 with smooth real-analytic boundary and non-compact automorphism group, which is not biholomorphically equivalent to any Reinhardt domain. We also give an analogous example in C, where the domain is bounded, non-pseudoconvex, is not equivalent to any Reinhardt domain, and the boundary is smooth real-analytic at al...

We give an example of a bounded, pseudoconvex, circular domain in Cn for any n ≥ 3 with smooth real-analytic boundary and non-compact automorphism group, which is not biholomorphically equivalent to any Reinhardt domain. We also give an analogous example in C, where the domain is bounded, non-pseudoconvex, is not equivalent to any Reinhardt domain, and the boundary is smooth real-analytic at al...

In this paper we prove that, if p is a boundary point of a smoothly bounded pseudoconvex Reinhardt domain in Cn, then the variety type at p is identical to the regular type. In this paper we study the finite type conditions on pseudoconvex Reinhardt domain. We prove that, if p is a boundary point of a smoothly bounded pseudoconvex Reinhardt domain in C, then the variety type at p is identical t...

The boundary behavior of the Bergman Kernel function of some Reinhardt domains is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points (z, z̄). Let D be the Reinhardt domain D = { z ∈ C | ‖z‖α = n ∑

We give a complete description of bounded Reinhardt domains of finite boundary smoothness that have non-compact automorphism group. As part of this program, we show that the classification of domains with non-compact automorphism group and having only finite boundary smoothness is considerably more complicated than the classification of such domains that have infinitely smooth boundary. Let D ⊂...

The Bohr radius for power series of holomorphic functions mapping Reinhardt domains D ⊂ C n into the convex domain G ⊂ C is independent of the domain G.

whenever |ζ1|, . . . , |ζn| ≤ 1 . In 1974 [11] Sunada investigated the structure of bounded Reinhardt domains containing the origin from the viewpoint of biholomorphic equivalence. He was able to describe completely the symmetric Reihardt domains which, up to linear isomomorphism, turned to be direct products of Euclidean balls. Our aim in this paper is to study infinite dimensional analogs of ...

It is shown that the Laurent series of a holomorphic function smooth up to boundary on Reinhardt domain in $${\mathbb {C}}^n$$ converges unconditionally Fréchet topology space functions boundary.

Let $\Omega$ be a bounded Reinhardt domain in $\mathbb{C}^n$ and $\phi_1,\ldots,\phi_m$ finite sums of quasi-homogeneous functions. We show that if the product Toeplitz operators $T_{\phi_m}\cdots T_{\phi_1}=0$ on Bergman space $\Omega$, then $\phi_j=0$ for some $j$.