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PRINTED BOOKS
Author Zygmund, Antoni, 1900-1992.

Title Trigonometric series / A. Zygmund.

Published New York : Cambridge University Press, 2002.

Copies

Location Call No. Status
 UniM Bund  515.2433 ZYGM {Bund89 20200519}    AVAILABLE
Edition [3rd ed.].
Physical description xiii, 383 pages, vii, 364 pages ; 23 cm.
Series Cambridge mathematical library.
Cambridge mathematical library.
Notes "Volumes I & II combined" -- Cover.
Bibliography Includes bibliographical references and index.
Contents Chapter I Trigonometric Series and Fourier Series. Auxiliary Results -- 1. Trigonometric series 1 -- 2. Summation by parts 3 -- 3. Orthogonal series 5 -- 4. Trigonometric system 6 -- 5. Fourier-Stieltjes series 10 -- 6. Completeness of the trigonometric system 11 -- 7. Bessel's inequality and Parseval's formula 12 -- 8. Remarks on series and integrals 14 -- 9. Inequalities 16 -- 10. Convex functions 21 -- 11. Convergence in L[superscript r] 26 -- 12. Sets of the first and second categories 28 -- 13. Rearrangements of functions. Maximal theorems of Hardy and Littlewood 29 -- Chapter II Fourier Coefficients. Elementary Theorems on The Convergence of S[f] and S[f] -- 1. Formal operations on S[f] 35 -- 2. Differentiation and integration of S[f] 40 -- 3. Modulus of continuity. Smooth functions 42 -- 4. Order of magnitude of Fourier coefficients 45 -- 5. Formulae for partial sums of S[f] and S[f] 49 -- 6. Dini test and the principle of localization 52 -- 7. Some more formulae for partial sums 55 -- 8. Dirichlet-Jordan test 57 -- 9. Gibbs's phenomenon 61 -- 10. Dini-Lipschitz test 62 -- 11. Lebesgue's test 65 -- 12. Lebesgue constants 67 -- 13. Poisson's summation formula 68 -- Chapter III Summability of Fourier Series -- 1. Summability of numerical series 74 -- 2. General remarks about the summability of S[f] and S[f] 84 -- 3. Summability of S[f] and S[f] by the method of the first arithmetic mean 88 -- 4. Convergence factors 93 -- 5. Summability (C, [alpha]) 94 -- 6. Abel summability 96 -- 8. Summability of S[dF] and S[dF] 105 -- 9. Fourier series at simple discontinuities 106 -- 10. Fourier sine series 109 -- 11. Gibbs's phenomenon for the method (C, [alpha]) 110 -- 12. Theorems of Rogosinski 112 -- 13. Approximation to functions by trigonometric polynomials 114 -- Chapter IV Classes of Functions and Fourier Series -- 1. Class L[superscript 2] 127 -- 2. A theorem of Marcinkiewicz 129 -- 3. Existence of the conjugate function 131 -- 4. Classes of functions and (c, 1) means of Fourier series 134 -- 6. Classes of functions and Abel means of Fourier series 149 -- 7. Majorants for the Abel and Cesaro means of s[f] 154 -- 8. Parseval's formula 157 -- 9. Linear operations 162 -- 10. Classes L*[subscript Phi] 170 -- 11. Conversion factors for classes of Fourier series 175 -- Chapter V Special Trigonometric Series -- 1. Series with coefficients tending montonically to zero 182 -- 2. Order of magnitude of functions represented by series with monotone coefficients 186 -- 3. A class of Fourier-Stieltjes series 194 -- 4. Series [Sigma]n[superscript -1/2-alpha] e[superscript icn log n] e[superscript inx] 197 -- 5. Series [Sigma]v[superscript -beta] e[superscript iv superscript alpha] e[superscript ivx] 200 -- 6. Lacunary series 202 -- 7. Riesz products 208 -- 8. Rademacher series and their applications 212 -- 9. Series with 'small' gaps 222 -- 10. A power series of Salem 225 -- Chapter VI Absolute Convergence of Trigonometric Series -- 1. General series 232 -- 2. Sets N 235 -- 3. Absolute convergence of Fourier series 240 -- 4. Inequalities for polynomials 244 -- 5. Theorems of Wiener and Levy 245 -- 6. Absolute convergence of lacunary series 247 -- Chapter VII Complex Methods in Fourier Series -- 1. Existence of conjugate functions 252 -- 2. Fourier character of conjugate series 253 -- 3. Applications of Green's formula 260 -- 4. Integrability B 262 -- 5. Lipschitz conditions 263 -- 6. Mean convergence of S[f] and S[f] 266 -- 7. Classes H[superscript p] and N 271 -- 8. Power series of bounded variation 285 -- 9. Cauchy's integral 288 -- 10. Conformal mapping 289 -- Chapter VIII Divergence of Fourier Series -- 1. Divergence of Fourier series of continuous functions 298 -- 2. Further examples of divergent Fourier series 302 -- 3. Examples of Fourier series divergent almost everywhere 305 -- 4. An everywhere divergent Fourier series 310 -- Chapter IX Riemann's Theory of Trigonometric Series -- 1. General remarks. The Cantor-Lebesgue theorem 316 -- 2. Formal integration of series 319 -- 3. Uniqueness of the representation by trigonometric series 325 -- 4. Principle of localization. Formal multiplication of trigonometric series 334 -- 5. Formal multiplication of trigonometric series (cont.) 337 -- 6. Sets of uniqueness and sets of multiplicity 344 -- 7. Uniqueness of summable trigonometric series 352 -- 8. Uniqueness of summable trigonometric series (cont.) 356 -- 9. Localization for series with coefficients not tending to zero 363.
Summary Both volumes of classic text on trigonometric series, now with a foreword by Robert Fefferman.
Subject Fourier series.
ISBN 0521890535 (paperback)