Synopses & Reviews
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 on a scale that limited the amount of detailed discussion possible. A greatly enlarged second edition (Cambridge, 1959) published in two volumes took full account of developments in trigonometric series, Fourier series, and related branches of pure mathematics since the publication of the original edition. These two volumes, bound together with a foreword from Robert Fefferman, outline the significance of this text. Volume I, containing the completely re-written material of the original work, deals with trigonometric series and Fourier series. Volume II provides much material previously unpublished in book form.
Review
'... much material previously unpublished in book form.' Zentralblatt MATH
Synopsis
Both volumes of classic text on trigonometric series, now with a foreword by Robert Fefferman.
Synopsis
Both volumes of classic text on trigonometric series, now with a foreword by Robert Fefferman.
Synopsis
Originally published in 1935, Professor Zygmund's Trigonometric Series rapidly established itself as a classic and has remained one of the most referenced works of mathematics ever since. Originally published separately, the two volumes were subsequently bound together as a single book. Volume I contains the basic material on trigonometric series and Fourier analysis, including the summability of Fourier series, special trigonometric series, complex methods in Fourier series, and Riemann's theory of trigonometric series. Volume II covers trigonometric interpolation, differentiation of series, convergence and summability, Fourier integrals and other advanced topics.
Synopsis
The third edition of Professor Zygmund's classic Trigonometric Series, now featuring a foreword by Robert Fefferman. Both volumes of the 1959 edition are bound as one. The rigorous treatment of this important subject presented here is a reference work of enduring value for mathematicians at graduate level and above.
Synopsis
This is the third edition of Professor Zygmund's classsic Trigonometric Series, now featuring a foreword by Elias Stein. Both volumes of the 1959 edition are here bound as one. Volume I, containing the completely re-written material of the original work, deals with trigonometric series and Fourier series. Volume II provides much material previously unpublished in book form. The rigorous treatment of trigonometric and Fourier series, and related branches of pure mathematics presented here is a reference work of enduring value for mathematicians at graduate level and above.
Table of 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.