An Interpolation Series for Continuous Functions of a p-adic Variable.
An Interpolation Series for Continuous Functions of a p-adic Variable.
复制标题
p 进变量连续函数的插值级数。
DOI：
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发表时间：
1958
期刊：
影响因子：
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通讯作者：
K. Mahler
中科院分区：
文献类型：
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作者：
K. Mahler
p 进变量的解析函数理论（即由幂级数定义的函数）比复杂解析函数的理论简单得多，并且几乎没有什么惊喜。另一方面，p 进变量的连续函数的行为与实连续函数的行为截然不同，并且实分析的许多基本定理没有 p 进类似物。因此，即使对于像 l l 这样的多项式，也没有与微分学的均值 ix 定理的简单模拟。存在无限多个
The theory of analytic functions of a p-adic variable (i. e. of functions defined by power series) is much simpler than that of complex analytic funktions and offers few surprises. On the other band, the behaviour of continuous functions of a p-adic variable is quite distinct from that of real continuous functions, and many basic theorems of real analysis have no p-adic analogues. Thus there is no simple analogue to the mean value ix theorem of differential calculus, even for polynomials like l l ; there exist infinitely many