Author | Butzer, Paul L. author |
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Title | Fourier Analysis and Approximation [electronic resource] : Vol. 1 One-Dimensional Theory / by Paul L. Butzer, Rolf J. Nessel |
Imprint | Basel : Birkhรคuser Basel, 1971 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-7448-9 |
Descript | XVI, 554 p. online resource |
0 Preliminaries -- 0 Preliminaries -- I Approximation by Singular Integrals -- 1 Singular Integrals of Periodic Functions -- 2 Theorems of Jackson and Bernstein for Polynomials of Best Approximation and for Singular Integrals -- 3 Singular Integrals on the Line Group -- II Fourier Transforms -- 4 Finite Fourier Transforms -- 5 Fourier Transforms Associated with the Line Group -- 6 Representation Theorems -- 7 Fourier Transform Methods and Second-Order Partial Differential Equations -- III Hilbert Transforms -- 8 Hilbert Transforms on the Real Line -- 9 Hilbert Transforms of Periodic Functions -- IV Characterization of Certain Function Classes 355 -- 10 Characterization in the Integral Case -- 11 Characterization in the Fractional Case -- V Saturation Theory -- 12 Saturation for Singular Integrals on X2? and Lp, 1 ? p ? 2 433 -- 13 Saturation on X(R) -- List of Symbols -- Tables of Fourier and Hilbert Transforms