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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 ]
In 1913 Toeplitz became an extraordinary professor at the University of Kiel. He was promoted to a professor in 1920. In 1911, Toeplitz proposed the inscribed square problem: Does every Jordan curve contain an inscribed square? This has been established for convex curves and smooth curves, but the question remains open in general (2007).
is called a Toeplitz system if is a Toeplitz matrix. If A {\displaystyle A} is an n × n {\displaystyle n\times n} Toeplitz matrix, then the system has at most only 2 n − 1 {\displaystyle 2n-1} unique values, rather than n 2 {\displaystyle n^{2}} .
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
Hilbert’s sixth problem was a proposal to expand the axiomatic method outside the existing mathematical disciplines, to physics and beyond. This expansion requires development of semantics of physics with formal analysis of the notion of physical reality that should be done. [9]
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)
The inscribed square problem, also known as the square peg problem or the Toeplitz' conjecture, is an unsolved question in geometry: Does every plane simple closed curve contain all four vertices of some square? This is true if the curve is convex or piecewise smooth and in other special cases. The problem was proposed by Otto Toeplitz in 1911. [1]
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