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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
Toeplitz matrices are persymmetric. Symmetric Toeplitz matrices are both centrosymmetric and bisymmetric. Toeplitz matrices are also closely connected with Fourier series, because the multiplication operator by a trigonometric polynomial, compressed to a finite-dimensional space, can be represented by such a matrix. Similarly, one can represent ...
Let () = be a sequence, and let = + + = = be its k th partial sum.. The sequence (a n) is called Cesàro summable, with Cesàro sum A ∈ , if, as n tends to infinity, the arithmetic mean of its first n partial sums s 1, s 2, ..., s n tends to A:
File information Description Toeplitz Classification of Mathematics Students in 1927 Source Mathematica 8.0 Date 2015-09-12 ... Version of PDF format: 1.5
Background Chlorine and caustic soda are produced at chlor-alkali plants using mercury cells or the increasingly popular membrane technology that is mercury free and more energy-
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