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In mathematics, a quasi-analytic class of functions is a generalization of the class of real analytic functions based upon the following fact. If ''f'' is an analytic function on an interval () ⊂ R, and at some point ''f'' and all of its derivatives are zero, then ''f'' is identically zero on all of (). Quasi-analytic classes are broader classes of functions for which this statement still holds true. ==Definitions== Let be a sequence of positive real numbers. Then we define the class of functions ''C''''M''(()) to be those ''f'' ∈ ''C''∞(()) which satisfy : for all ''x'' ∈ (), some constant ''A'', and all non-negative integers ''k''. If ''M''''k'' = ''k''! this is exactly the class of real analytic functions on (). The class ''C''''M''(()) is said to be ''quasi-analytic'' if whenever ''f'' ∈ ''C''''M''(()) and : for some point ''x'' ∈ () and all ''k'', ''f'' is identically equal to zero. A function ''f'' is called a ''quasi-analytic function'' if ''f'' is in some quasi-analytic class. 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「Quasi-analytic function」の詳細全文を読む スポンサード リンク
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