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In mathematics, the Silverman–Toeplitz theorem, first proved by Otto Toeplitz, is a result in series summability theory characterizing matrix summability methods that are regular. A regular matrix summability method is a linear sequence transformation that preserves the limits of convergent sequences . [ 1 ]
The Silverman–Toeplitz theorem characterizes matrix summation methods, which are methods for summing a divergent series by applying an infinite matrix to the vector of coefficients. The most general methods for summing a divergent series are non-constructive and concern Banach limits .
Toeplitz algebra, the C*-algebra generated by the unilateral shift on the Hilbert space; Toeplitz Hash Algorithm, used in many network interface controllers; Hellinger–Toeplitz theorem, an everywhere defined symmetric operator on a Hilbert space is bounded; Silverman–Toeplitz theorem, characterizing matrix summability methods which are regular
Otto Toeplitz and Alexander Ostrowski. Toeplitz was born to a Jewish family of mathematicians. Both his father and grandfather were Gymnasium mathematics teachers and published papers in mathematics. Toeplitz grew up in Breslau and graduated from the Gymnasium there.
Siegel–Walfisz theorem (analytic number theory) Silverman–Toeplitz theorem (mathematical analysis) Simplicial approximation theorem (algebraic topology) Sinkhorn's theorem (matrix theory) Sion's minimax theorem (game theory) Sipser–Lautemann theorem (probabilistic complexity theory) (structural complexity theory)
An Toeplitz matrix may be defined as a matrix where , =, for constants , …,.The set of Toeplitz matrices is a subspace of the vector space of matrices (under matrix addition and scalar multiplication).
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Download as PDF; Printable version; In other projects ... Silverman–Toeplitz theorem; Stolz–Cesàro theorem; Cauchy's limit theorem;