The Bergman kernel function for intersections of some cylindrical domains and Lauricella's hypergeometric function
| Autor: | Jong Do Park |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Applied Mathematics
010102 general mathematics Diagonal Boundary (topology) Function (mathematics) 01 natural sciences 010101 applied mathematics Combinatorics Intersection Domain (ring theory) 0101 mathematics Connection (algebraic framework) Hypergeometric function Analysis Mathematics Bergman kernel |
| Zdroj: | Journal of Mathematical Analysis and Applications. 504:125398 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2021.125398 |
| Popis: | In this paper, we show that Lauricella's hypergeometric function F 8 has a close connection with the Bergman kernel for the intersection of two cylindrical domains defined by D ( p 1 , p 2 , p 3 ) : = { z ∈ C 3 : | z 1 | 2 p 1 + | z 2 | 2 p 2 1 , | z 1 | 2 p 1 + | z 3 | 2 p 3 1 } . We investigate the boundary behavior of the Bergman kernel on the diagonal ( z 1 , 0 , 0 ) . We also compute the explicit form of the Bergman kernel when ( p 1 , p 2 , p 3 ) = ( 1 , p 2 , p 3 ) and ( p , 1 , 1 ) . As a consequence, we show that D ( 1 , p 2 , p 3 ) is a Lu Qi-Keng domain. All results can be generalized to the intersection of cylindrical domains in any higher dimension. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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