Singularities of the Bergman Kernel for Certain Weakly Pseudoconvex Domains

Journal of Mathematical Sciences

Kamimoto, Joe¹ 

关键词: Bergman kernel;    Szegö kernel;    weakly pseudoconvex domain of finite type;    polar coordinates;    irregular singular point;    admissible approach region;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

ConsidertheBergmankernel$K^B(z)$ofthedomain$ellip={zinComp^n;sum_{j=1}^n|z_j|^{2m_j}<1}$,where$m=(m_1,ldots,m_n)inNatl^n$and$m_neq1$.Let$z^0inpartialellip$beanyweaklypseudoconvexpoint,$kinNatl$thedegeneraterankoftheLeviformat$z^0$.Anexplicitformulafor$K^B(z)$moduloanalyticfunctionsisgivenintermsofthepolarcoordinates$(t_1,ldots,t_k,r)$around$z^0$.Thisformulaprovidesdetailedinformationaboutthesingularitiesof$K^B(z)$,whichimprovestheresultofA.BonamiandN.Lohouécite{bol}.AsimilarresultisestablishedalsofortheSzegökernel$K^S(z)$of$ellip$.

【 授权许可】

Unknown