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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 ]
Otto Toeplitz. Here is how Gottfried Köthe, who was Toeplitz's assistant in Bonn, described their collaboration: Otto liked to take walks and talk about scientific questions. I in fact needed a piece of paper and pencil to write everything down. Toeplitz convinced me that the great outline of research comes to light best in dialog.
Silverman–Toeplitz theorem; Summation by parts; Z. Zeldovich regularization; Zeta function regularization This page was last edited on 9 January 2014, at 19:17 (UTC ...
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 linear convolution as multiplication by a Toeplitz matrix. Toeplitz matrices commute asymptotically.
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
Silverman is a lifelong animal lover. Ever since witnessing the death of a Thanksgiving turkey as a child, Silverman has been a vegetarian, with a brief attempt at veganism in 2021.
Silverman–Toeplitz theorem; U. Unconditional convergence This page was last edited on 11 October 2010, at 18:00 (UTC). Text is available under the Creative ...