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Zbl 0989.41504
Lorentz, G.G.
Bernstein polynomials. 2nd ed. (English)
[B] New York, NY: Chelsea Publishing. x, 134 p. \$ 15.00 (1986). ISBN 0-8284-0323-6/hbk

From the preface: 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 (Univ. Toronto Press, Toronto, Ont., 1953; Zbl 0051.05001), 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 1953. I am very grateful to Chelsea Publishing Company for their suggestion that a second edition of my book be published.\par Some of the theorems of the book were original results at the time. I will mention here: new proofs of the theorems of F. Riesz (page 63) and of Halperin (page 71); the interpolation theorem for operators on page 78 (the same proof also gives the more general theorem of Mityagin and Caldéron); the new form of Okada's theorem on page 119; and---perhaps most important---the new exposition of Bernstein's theory in the complex field, on pages 88-117.

MSC 2000:: *41A10 Approximation by polynomials
41-02 Research monographs (approximations and expansions)

Citations: Zbl 0051.05001

Cited in: Zbl 1183.41006 Zbl 1183.33021

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	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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