Weierstrass and Approximation Theory

By Allan Pinkus. 2000

110 citations recorded by the source corpus.

Subfields: Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/2240f45aae31f3abba429ecf6ca392675940f1bb

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In Computer Networks and Communications

Citations in the corpus

The Bernstein polynomial basis: A centennial retrospective (2012, background): “Pinkus [155] describes in detail the contributions of Weierstrass to approximation theory.”
Holomorphic Approximation: The Legacy of Weierstrass, Runge, Oka–Weil, and Mergelyan (2018, background): “rmly on compact intervals in R. If furthermore f is of class Ck,thenbyachangeofvariableu=x−zandplacingthederivativeson f itfollows that we get convergencealso in the Ck norm. ⊓⊔ The paperby A. Pinkus [136] (2000)containsa more completesurveyof Weierstrass’s results and of his impact on the theory of”
The Takagi function and its properties (Functions in Number Theory and Their Probabilistic Aspects) (2011, background): “ivative at any point. The example of Takagi is much simpler, and has no point with a nite derivative, but it does have some points with a well-dened innite derivative, see Theorem 8.6 below. Pinkus [70] gives additional history on this problem. 2 In 1918 Knopp [50] studied many variants of non-diere”
Continuous Nowhere Differentiable Functions (2003, background): “Ampère even tried to give a theoretical justification for this statement in 1806 (cf. Ampère [1]), although it is not exactly clear 1Quote borrowed from Pinkus [57].”
Korovkin-type Theorems and Approximation by Positive Linear Operators (2010, background): “orem 3.6 furnishes a constructive proof of the Weierstrass approximation theorem [119] which we state below. (For a survey on many other alternative proofs of Weierstrass’ theorem, we refer, e.g., to [93, 94].) Theorem 3.7. For every f ∈ C([0,1]), there exists a sequence of algebraic polynomials tha”
A survey on the Weierstrass approximation theorem (2006, background): “The proofs more commonly taken at level of undergraduate courses in Mathematics are those of Fejér (1900) and Bernstein (1912) (see, for example [4], [7], [16] or [20]).”
A chronology of interpolation: from ancient astronomy to modern signal and image processing (2002, background): “24For more detailed information on the development of approximation theory, see the recently published historical review by Pinkus [85].”