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 Volume II provides much material previously unpublished in book form.
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'... much material previously unpublished in book form.' Zentralblatt MATH
Book Description
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 Volume II provides much material previously unpublished in book form.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.
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10 of 11 people found the following review helpful:
5.0 out of 5 stars
aging but still a milestone anyway,
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This review is from: Trigonometric Series (Cambridge Mathematical Library) (Paperback)
I am very surprised to be the first person to write a review on this widely known reference in trigonometric and fourier series; there is nothing much to
say: this is a definite reference although things have certainly changed a bit since the last time the author did work on it. I found both books in hardback edition lately at a much cheaper price than as a new paperback and I had an instant use of it when asked a specific question on a math forum by a student... Definitely belongs to the "Hardy-Littlewood" and "Polya-Szëgo" type but then all the more respectable. By the way, Zygmund wrote a reference book together with Saks on analytic functions...
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Inside This Book
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First Sentence:
Here x is a real variable and the coefficients a0, a1, b1, ... are independent of x. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
equiconvergence theorems, second indefinite integral, miscellaneous theorems, strong summability, first arithmetic mean, essential upper bound, lacunary series, power series type, lacunary trigonometric series, integrated termwise, conjugate series, regular discontinuities, interval contiguous, series conjugate, intervals contiguous, formal multiplication, conjugate kernel, trigonometric system, symmetric derivative, convergent trigonometric series, strong differentiability, series summable, cosine polynomial, trigonometric integrals, trigonometrical series Key Phrases - Capitalized Phrases (CAPs): (learn more)
Divergence of Fourier, Theory of the Integral, Using Theorem New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Here x is a real variable and the coefficients a0, a1, b1, ... are independent of x. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
equiconvergence theorems, second indefinite integral, miscellaneous theorems, strong summability, first arithmetic mean, essential upper bound, lacunary series, power series type, lacunary trigonometric series, integrated termwise, conjugate series, regular discontinuities, interval contiguous, series conjugate, intervals contiguous, formal multiplication, conjugate kernel, trigonometric system, symmetric derivative, convergent trigonometric series, strong differentiability, series summable, cosine polynomial, trigonometric integrals, trigonometrical series Key Phrases - Capitalized Phrases (CAPs): (learn more)
Divergence of Fourier, Theory of the Integral, Using Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 12
books:
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100
books
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- Theory of the Integral (Dover Books on Mathematics) by Stanislaw Saks on page 308, page 327, and page 361
- Fouriersche Integrale by Salomon Bochner in Back Matter (1), and Back Matter (2)
- Divergent Series (AMS Chelsea Publishing) by G. H. Hardy in Back Matter (1), and Back Matter (2)
- Fourier Series by G. H. Hardy in Back Matter (1), and Back Matter (2)
- Waves in Fluids (Cambridge Mathematical Library) by James Lighthill in Front Matter
See all 12 books this book cites
- Conference on Harmonic Analysis in Honor of Antoni Zygmund (The Wadsworth Mathematics Series) by Pedro Calderón de la Barca on 10 pages
- Wavelet Analysis and Multiresolution Methods (Lecture Notes in Pure and Applied Mathematics) by Tian-Xiao He on page 47, page 298, and page 316
- Probability for Analysts (Chapman & Hall/CRC Probability Series) by Karl R. Stromberg on page 17, page 214, and page 306
- Basic Real Analysis by Anthony W. Knapp in Front Matter, page 613, and Back Matter
- Fourier Analysis and Approximation of Functions by Roald M. Trigub in Back Matter (1), and Back Matter (2)
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