The Zeros of the Bergman Kernel for Some Reinhardt Domains
Author
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-10-09
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We consider the Reinhardt domain Dn={(ζ,z)∈C×Cn:|ζ|2<(1-|z1|2)⋯(1-|zn|2)}.
We express the explicit closed form of the Bergman kernel for Dn using the exponential generating function for the Stirling number of the second kind.
As an application, we show that the Bergman kernel Kn for Dn has zeros if and only if n≥3.
The study of the zeros of Kn is reduced to some real polynomial with coefficients which are related to Bernoulli numbers.
This result is a complete characterization of the existence of zeros of the Bergman kernel for Dn for all positive integers n.
American Psychological Association (APA)
Park, Jong-Do. 2016. The Zeros of the Bergman Kernel for Some Reinhardt Domains. Journal of Function Spaces،Vol. 2016, no. 2016, pp.1-9.
https://search.emarefa.net/detail/BIM-1108599
Modern Language Association (MLA)
Park, Jong-Do. The Zeros of the Bergman Kernel for Some Reinhardt Domains. Journal of Function Spaces No. 2016 (2016), pp.1-9.
https://search.emarefa.net/detail/BIM-1108599
American Medical Association (AMA)
Park, Jong-Do. The Zeros of the Bergman Kernel for Some Reinhardt Domains. Journal of Function Spaces. 2016. Vol. 2016, no. 2016, pp.1-9.
https://search.emarefa.net/detail/BIM-1108599
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1108599
