Fourier analysis and approximation

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Page iii

Copyright page
Page iv

Preface
Pages vii-ix
P.L. Butzer, R.J. Nessel

0 Preliminaries
Pages 1-24

Part I Approximation by Singular Integrals
Pages 25-28

1 Singular Integrals of Periodic Functions
Pages 29-93

2 Theorems of Jackson and Bernstein for Polynomials of Best Approximation and for Singular Integrals
Pages 94-118

3 Singular Integrals on the Line Group
Pages 119-161

Part II Fourier Transforms
Pages 163-166

4 Finite Fourier Transforms
Pages 167-187

5 Fourier Transforms Associated with the Line Group
Pages 188-230

6 Representation Theorems
Pages 231-277

7 Fourier Transform Methods and Second-Order Partial Differential Equations
Pages 278-302

Part III Hilbert Transforms
Pages 303-304

8 Hilbert Transforms on the Real Line
Pages 305-333

9 Hilbert Transforms of Periodic Functions
Pages 334-354

Part IV Characterization of Certain Function Classes
Pages 355-356

10 Characterization in the Integral Case
Pages 357-390

11 Characterization in the Fractional Case
Pages 391-430

Part V Saturation Theory
Page 431

12 Saturation for Singular Integrals on X2π and Lp, 1 ≤ p ≤ 2
Pages 433-482

13 Saturation on X(R)
Pages 483-509

List of Symbols
Pages 511-514

Tables of Fourier and Hilbert Transforms
Pages 515-520

Bibliography
Pages 521-546

Index
Pages 547-553

Pure and Applied Mathematics A Series of Monographs and Textbooks
Pages 554-555