为讨论调和整映射的增长估计,研究其级和型,而级和型可以由其解析部分以及反解析部分的系数刻画.对于严格递增的正整数数列{nk}∞k=1,利用调和整映射的解析部分和反解析部分的nk阶导数在某一点的值,定义了2个量,且证明了这2个量分别与调和整映射的级和型几乎处处相等.
In order to discuss the growth estimates of harmonic entire mappings, the order and the type of harmonic entire mappings are studied, and they can be characterized by the coefficients of the analytic parts and anti-analytic parts. For a strictly increasing sequence of positive integers{nk}∞k=1, two quantities are defined by using the values of nk order derivative of the analytic part and anti-analytic part of a harmonic entire mapping at a certain point, and it is proved that these two quantities are equal to the order and the type of the harmonic entire mapping, respectively, almost everywhere.
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