一類Hartogs域的Bergman核函數(shù)

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【Abstract]TheBergmankernelfunctionplaysanimportantroleinthetheoryofseveralcomplex variables.This paperconstructsanewclassofHartogsdomainsand，byemploying methodsfromcomplexanalysisandseveralcomplexvariablesheo ry，utilizesseries expansionsandthetransformationruleoftheBergmankernelunderbiholomorphicmappings toderivethe diffrentialrelationshipbetweenthe Bergmankerelsof thesedomainsandtheirbasedomains.Thisapproachprovidesa more straightforward method for computing the Bergman kernel functions on certain domains.

【Key words] Hartogs domain; Bergman kernel; starlike domain

[中圖分類號(hào)]0174.55 [文獻(xiàn)標(biāo)識(shí)碼］A

[文章編號(hào)]1674-3229（2025）02-0016-07

0 引言

Bergman核函數(shù)的概念是波蘭著名數(shù)學(xué)家S.Bergman于20世紀(jì)20年代在研究平面區(qū)域之間的共形映照時(shí)引進(jìn)的。（剩余5575字）