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:''Not to be confused with Carleson's theorem'' In mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem which was discovered by Fritz David Carlson. Informally, it states that two different analytic functions which do not grow very fast at infinity can not coincide at the integers. The theorem may be obtained from the Phragmén–Lindelöf theorem, which is itself an extension of the maximum-modulus theorem. Carlson's theorem is typically invoked to defend the uniqueness of a Newton series expansion. Carlson's theorem has generalized analogues for other expansions. ==Statement of theorem== Assume that ''f'' satisfies the following three conditions: the first two conditions bound the growth of ''f'' at infinity, whereas the third one states that ''f'' vanishes on the non-negative integers. * is an entire function of exponential type, meaning that :: :for some * There exists such that :: * (''n'') = 0 for any non-negative integer ''n''. Then is identically zero. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Carlson's theorem」の詳細全文を読む スポンサード リンク
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