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Theory of Approximation (Dover Books on Mathematics), by N. I. Achieser
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A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of problems and applications (elementary extremal problems, Szego's theorem, the Carathéodory-Fejér problem, and more).
- Sales Rank: #1915746 in eBooks
- Published on: 2013-06-05
- Released on: 2013-06-05
- Format: Kindle eBook
Language Notes
Text: English (translation)
Original Language: Russian
Most helpful customer reviews
11 of 11 people found the following review helpful.
The fundamentals.
By Palle E T Jorgensen
Even at a time when a subject undergoes a revolution, and new directions keep coming, new methods; even brand new and different applications--- even then are there central ideas that are constant, the fundamentals. Within mathematics, approximation theory is such a field: In the past decade, we have seen a host of such new developments: wavelet approximations, fast computational algorithms with applications to turbulence, chaos and fractals; computational efficiencies from scaling similarities, and data compression; and new adaptive non-linear algorithms. The author Achieser of this Dover classic (first published by Ungar in 1956, and reprinted by Dover in 1992) is a pioneer in the approximation theory, and the book is still a very attractive first. I recommend it to students even today! Achieser's lovely book begins with the fundamentals on normed spaces, and it has the classical theorems of Weierstrass, Muntz, and Riesz. The other topics range from the incisive ideas of Tchebysheff and Haar to harmonic approximation. From extremal properties of transcendental functions to Wiener's general Tauber theorem, and more.
Review by Palle Jorgensen, October 2003.
9 of 9 people found the following review helpful.
an encyclopedia of results in approximation theory
By UNPINGCO
This should be on the reading list of every graduate student in control or signal processing. This book is an encyclopedia of results in approximation theory including Chebyshev approximation, harmonic analysis, and extremal properties of integral transcendental functions. The exposition is terse in some places and the proofs are sometimes sketchy, but the examples are really great. The focus on the ideas is excellent.
2 of 4 people found the following review helpful.
An excellent book on approximation theory
By Faton Berisha
An excellent, graduate level, reference book on approximation theory.
Different aspects of relations between constructive and structural properties of functions studied.
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