Let Gi be a closed Lie subgroup of U（n）, Ωi be a bounded Gi-invariant domain in Cn which contains 0, and （9（Cn）Gi = C, for i= 1,2. If f ： f21 →2 is abiholomorphism, and f（0） = 0, then f is a polynomial mappi...Let Gi be a closed Lie subgroup of U（n）, Ωi be a bounded Gi-invariant domain in Cn which contains 0, and （9（Cn）Gi = C, for i= 1,2. If f ： f21 →2 is abiholomorphism, and f（0） = 0, then f is a polynomial mapping （see Ning et al. （2017））. In this paper, we provide an upper bound for the degree of such polynomial mappings. It is a natural generalization of the well-known Cartan＇s theorem.展开更多
基金partially supported by the NSFC grant (12071485)partially supported by the Beijing Natural Science Foundation (1202012,Z190003)+1 种基金the NSFC grant (11701031,12071035)partially supported by the NSFC grant (11688101)。
基金supported by National Natural Science Foundation of China(Grant Nos.11501058 and 11431013)the Fundamental Research Funds for the Central Universities(Grant No.0208005202035)Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZDY-SSW-SYS001)
文摘Let Gi be a closed Lie subgroup of U（n）, Ωi be a bounded Gi-invariant domain in Cn which contains 0, and （9（Cn）Gi = C, for i= 1,2. If f ： f21 →2 is abiholomorphism, and f（0） = 0, then f is a polynomial mapping （see Ning et al. （2017））. In this paper, we provide an upper bound for the degree of such polynomial mappings. It is a natural generalization of the well-known Cartan＇s theorem.
