Bernstein Polynomials

Portada
American Mathematical Soc., 2012 - 134 pàgines

Bernstein polynomials are a remarkable family of polynomials associated to any given function on the unit interval. Their first notable appearance was in Bernstein's proof of the Weierstrass approximation theorem. This book gives an exhaustive exposition of the main facts about the Bernstein polynomials and discusses some of their applications in analysis. The first three chapters of the book give an introduction to a theory of singular integrals by means of the particular instance of Bernstein polynomials.

The author writes in the preface to this second edition, "After the trigonometric integrals, Bernstein polynomials are the most important and interesting concrete operators on a space of continuous functions. Since the appearance of the first edition of this book [in 1953], the interest in this subject has continued. In an appendix we have summed up a few of the most important papers that have appeared since."

 

Continguts

I
5
II
30
III
52
IV
87
Copyright

Altres edicions - Mostra-ho tot

Bernstein Polynomials
G. G. Lorentz
Visualització de fragments - 1953
Bernstein Polynomials
G. G. Lorentz
Previsualització no disponible - 1986

Frases i termes més freqüents

analytic angle approximation arbitrary assume Banach Banach space belong Bernstein polynomials boundary bounded branch called circle closed coefficients complete condition consider constant contains continuous function convergence convex corresponding curve decreasing deduce defined definition denote derivative discuss elements equal equation example exceed exists expression fact finite first fixed follows formula function f give given hand Hence holds implies important inequality inside instance integral interval limit linear functional loop Lorentz matrix means measurable functions method moment problem necessary norm obtain particular points of intersection positive problem proof properties prove region regular relation remark replaced respect satisfies satisfying segment sequence shows side space sufficient summation Suppose tangent term theorem true uniformly values variation zero

Informació bibliogràfica

TítolBernstein Polynomials
AMS Chelsea Publishing
AutorG. G. Lorentz
Edicióil·lustrada
EditorAmerican Mathematical Soc., 2012
ISBN0821875582, 9780821875582
Nre. de pàgines134 pàgines
  
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