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In mathematics, and specifically in operator theory, a positive-definite function on a group relates the notions of positivity, in the context of Hilbert spaces, and algebraic groups. It can be viewed as a particular type of positive-definite kernel where the underlying set has the additional group structure. == Definition == Let ''G'' be a group, ''H'' be a complex Hilbert space, and ''L''(''H'') be the bounded operators on ''H''. A positive-definite function on ''G'' is a function that satisfies : for every function ''h'': ''G'' → ''H'' with finite support (''h'' takes non-zero values for only finitely many ''s''). In other words, a function ''F'': ''G'' → ''L''(''H'') is said to be a positive definite function if the kernel ''K'': ''G'' × ''G'' → ''L''(''H'') defined by ''K''(''s'', ''t'') = ''F''(''s''−1''t'') is a positive-definite kernel. 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「Positive-definite function on a group」の詳細全文を読む スポンサード リンク
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