A generalization of the Forelli-Rudin construction and deflation identities

Yamamori, Atsushi

doi:10.1090/s0002-9939-2014-12317-3

Cited by 4 publications

(5 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In our previous paper [32], we obtained a generalization of the Forelli-Rudin construction. Let P be a real valued continuous function on C m and α = (α 1 , .…”

Section: Forelli-rudin Constructionmentioning

confidence: 99%

See 1 more Smart Citation

Non-hyperbolic unbounded Reinhardt domains: non-compact automorphism group, Cartan's linearity theorem and explicit Bergman kernel

Yamamori¹

2017

Tohoku Math. J. (2)

Self Cite

View full text Add to dashboard Cite

In the study of the holomorphic automorphism groups, many researches have been carried out inside the category of bounded or hyperbolic domains. On the contrary to these cases, for unbounded non-hyperbolic cases, only a few results are known about the structure of the holomorphic automorphism groups. Main result of the present paper gives a class of unbounded non-hyperbolic Reinhardt domains with non-compact automorphism groups, Cartan's linearity theorem and explicit Bergman kernels. Moreover, a reformulation of Cartan's linearity theorem for finite volume Reinhardt domains is also given. Introduction.In several complex variables, complex domains with properties boundedness or hyperbolicity are fundamental research objects. On the other hand, one may not expect some useful function-theoretic properties for complex domains without the two properties. Our primary motivation is to investigate some useful properties for unbounded non-hyperbolic domains.1.1. Background. One of the most important problem in several complex variables is to classify all complex domains in C n . If n = 1, then the Riemann mapping theorem tells us that every simply connected proper subdomain of C is biholomorphically equivalent to the unit disk. By showing the inequivalence of the unit ball and the polydisk in C 2 , Poincaré found that the Riemann mapping theorem does not hold even simply connected domains in C 2 . Thus the purely topological condition "simply connectedness" is not enough for the holomorphic equivalence problem in C n . Because of this background, in several complex variables, it is important to investigate biholomorphic invariant objects of complex domains.The purpose of this paper is to study two objects (the holomorphic automorphism group and the Bergman kernel) for a certain class of non-hyperbolic unbounded Reinhardt domains. The holomorphic automorphism group is a biholomorphic invariant object. Moreover, from the Bergman kernel, one can construct an invariant metric which is so-called the Bergman metric. In the theory of the automorphism groups, one important problem is to understand how the information of the holomorphic automorphism group characterizes complex domains. The next theorem is a notable result concerning this problem (cf.

show abstract

“…In our previous paper [32], we obtained a generalization of the Forelli-Rudin construction. Let P be a real valued continuous function on C m and α = (α 1 , .…”

Section: Forelli-rudin Constructionmentioning

confidence: 99%

“…In [32], this formula is applied to establish deflation type identities which is initiated by Boas-Fu-Straube…”

Section: Forelli-rudin Constructionmentioning

confidence: 99%

Non-hyperbolic unbounded Reinhardt domains: non-compact automorphism group, Cartan's linearity theorem and explicit Bergman kernel

Yamamori¹

2017

Tohoku Math. J. (2)

Self Cite

View full text Add to dashboard Cite

show abstract

“…where D is an irreducible bounded symmetric domain in C d . Another generalization of the Forelli-Rudin construction is also achieved by the second author [20]; precisely, a main object is in exploring the following domain…”

Section: Preliminariesmentioning

confidence: 99%

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

Kim

Yamamori

2015

Bulletin des Sciences Mathématiques

Self Cite

View full text Add to dashboard Cite

show abstract

“…. , p m ∈ Z + (see [4] and [27]). Another direction for a generalization of the Hartogs domain has been also considered by several authors.…”

Section: Introductionmentioning

confidence: 99%

“…The Forelli-Rudin construction is generalized for Ω m,p in [27]. If Ω is an irreducible bounded symmetric domain F and Φ is the generic norm of F , then this domain is called the Hua domain.…”

Section: Introductionmentioning

confidence: 99%

The holomorphic automorphism groups of twisted Fock-Bargmann-Hartogs domains

Kim

Yamamori

2018

Czech.Math.J.

Self Cite

View full text Add to dashboard Cite

show abstract

A generalization of the Forelli-Rudin construction and deflation identities

Abstract: We establish a series representation formula of the Bergman kernel of a certain class of domains, which generalizes the Forelli-Rudin construction of the Hartogs domain. Our formula is applied to derive deflation type identities of the Bergman kernels for our domains.

Cited by 4 publications

References 22 publications

Non-hyperbolic unbounded Reinhardt domains: non-compact automorphism group, Cartan's linearity theorem and explicit Bergman kernel

Non-hyperbolic unbounded Reinhardt domains: non-compact automorphism group, Cartan's linearity theorem and explicit Bergman kernel

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

The holomorphic automorphism groups of twisted Fock-Bargmann-Hartogs domains

Contact Info

Product

Resources

About