On an Algebraic Problem Related to an Analytic Theorem of Carathéodory and Fdjér and on an Allied Theorem of Landau
On an Algebraic Problem Related to an Analytic Theorem of Carathéodory and Fdjér and on an Allied Theorem of Landau
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与卡拉西奥多里和费杰尔解析定理相关的代数问题及朗道联合定理
DOI：
10.11429/ppmsj1919.6.10_130
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通讯作者：
T. Takagi
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作者：
T. Takagi
对于任何其他解析函数f（z），正则为|z|其中在z= 0处的泰勒级数在前n+ 1项与F（z）重合，|f（z）|在圈内|z| < 1大于m。原来的证明，它的作者已经给出的定理，是基于性质的凸域在一个2n维空间。Schur（3）给出了一个更直接的证明。这里讨论的有理函数的形式是，
For any other analytie function f (z), regular for| z|< 1, of which the Taylor-series at z= 0 coincides with F (z) in the first n+ 1 terms, the upper limit of| f (z)| in the circle| z|< 1 is greater than m. The original proof, which its authors have given of the theorem, is based on the property of a convex domain in a 2n-dimensional space. A more direct proof has been given by Schur (3). The rational function in question is of the form where and such that all roots of the equation