Search results
Results From The WOW.Com Content Network
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 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:
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. 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.
In his nearly four weeks in office, President Donald Trump has unveiled a constant stream of policy priorities in quick succession, from shrinking government, to cutting taxes, to waging a war on ...
In mathematical analysis, the Szegő limit theorems describe the asymptotic behaviour of the determinants of large Toeplitz matrices. [ 1 ] [ 2 ] [ 3 ] They were first proved by Gábor Szegő . Notation