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In mathematics, the Silverman–Toeplitz theorem, first proved by Otto Toeplitz, is a result in summability theory characterizing matrix summability methods that are regular. A regular matrix summability method is a matrix transformation of a convergent sequence which preserves the limit. An infinite matrix (every column sequence converges to 0) : (the row sums converge to 1) : (the absolute row sums are bounded). == References == * Toeplitz, Otto (1911) "(''Über die lineare Mittelbildungen.'' )" ''Prace mat.-fiz.'', 22, 113–118 (the original paper in German) * Silverman, Louis Lazarus (1913) "On the definition of the sum of a divergent series." University of Missouri Studies, Math. Series I, 1–96 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「Silverman–Toeplitz theorem」の詳細全文を読む スポンサード リンク
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