Trigonometric Series: Volumes I & II Combines

ISBN-13: 9780521890533 / Angielski / Miękka / 2003 / 784 str.

A. Zygmund; Robert A. Fefferman; Antoni Zygmund

Opis

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 Volume II provides much material previously unpublished in book form.

Recenzje

'... much material previously unpublished in book form.' Zentralblatt MATH

Spis treści

Part I: 1. Trigonometric series and Fourier series, auxilliary results; 2. Fourier coefficients, elementary theorems on the convergence of S[f] and \tilde[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.