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Trigonometric Series (Cambridge Mathematical Library) (3rd Revised edition)
Professor Zygmund's Trigonometric Series, first published in Warsaw in 1935, established itself as a classic. It presented a concise account of the main results then known, but was on a scale which limited the amount of detailed discussion possible. A greatly enlarged second edition published by Cambridge in two volumes in 1959 took full account of
developments in trigonometric series, Fourier series and related branches of pure mathematics since the publication of the original edition. The two volumes are here bound together with a foreword from Robert Fefferman outlining the significance of this text. Volume I, containing the completely rewritten material of the original work, deals with trigonometric series and Fourier series. Volume II provides much material previously unpublished in book form.
Contents:
Part I: 1
Trigonometric series and Fourier series, auxilliary results
- 2
Fourier coefficients, elementary theorems on the convergence of S[f] and \tilde{S}[f]
- 3
Summability of Fourier series
- 4
Classes of functions and Fourier series
- 5
Special trigonometric series
- 6
The absolute convergence of trigonometric series
- 7
Complex methods in Fourier series
- 8
Divergence of Fourier series
- 9
Riemann's theory of trigonometric series
- Part II: 10
Trigonometric interpolation
- 11
Differentiation of series, generalised derivatives
- 12
Interpolation of linear operations, more about Fourier coefficients
- 13
Convergence and summability almost everywhere
- 14
More about complex methods
- 15
Applications of the Littlewood-Paley function to Fourier series
- 16
Fourier integrals
- 17
A topic in multiple Fourier series.
Brief Description:
Both volumes of classic text on trigonometric series, now with a foreword by Robert Fefferman.
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