The Bergman kernel: Explicit formulas, deflation, Lu Qi-Keng problem and Jacobi polynomials

Title:

The Bergman kernel: Explicit formulas, deflation, Lu Qi-Keng problem and Jacobi polynomials

Creator:

Beberok, Tomasz

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7ea54923-b451-4701-83fb-4400153ef491
uuid:7ea54923-b451-4701-83fb-4400153ef491
issn:0011-4642

Subject:

matematika, mathematics, Jacobi polynomial, Lu Qi-Keng problem, Bergman kernel, Routh-Hurwitz theorem, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

We investigate the Bergman kernel function for the intersection of two complex ellipsoids {(z,w1,w2) 2 Cn+2 : |z1|2+. . .+|zn|2+|w1|q <1, |z1|2+. . .+|zn|2+|w2|r < 1}. We also compute the kernel function for {(z1,w1,w2) 2 C3 : |z1|2/n + |w1|q < 1, |z1|2/n + |w2|r < 1} and show deflation type identity between these two domains. Moreover in the case that q = r = 2 we express the Bergman kernel in terms of the Jacobi polynomials. The explicit formulas of the Bergman kernel function for these domains enables us to investigate whether the Bergman kernel has zeros or not. This kind of problem is called a Lu Qi-Keng problem., Tomasz Beberok., and Seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

537-549

Source:

Czechoslovak Mathematical Journal | 2017 Volume:67 | Number:2

Harvested from:

CDK

Metadata only:

false