On the Singularities of Non-Analytic Szegö Kernels

Journal of Mathematical Sciences

Kamimoto, Joe¹ 

关键词: Szegö kernel;    Bergman kernel;    weakly pseudoconvex;    of finite type;    analytically hypoelliptic;    CR manifold;    Borel sum;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

The,,{itCR},,manifold,,$M_m=,,{(z_1,z_2),in,{mathbbC}^2;,,Imz_2=[Rez_1]^{2m}}(m=2,3,ldots)$isacounterexample,whichwasgivenbyChristandGeller,toanalytichypoellipticityof$ar{partial}_{b}$andrealanalyticityoftheSzegökernel.InordertogiveadirectinterpretationforthebreakdownofrealanalyticityoftheSzegökernel,wegiveaBorelsummationtyperepresentationoftheSzegökernelintermsofsimplesingularsolutionsoftheequation$ar{partial}_{b}u=0$.

【 授权许可】

Unknown