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Part V Saturation Theory
Part V Saturation Theory
This Part is devoted to a study of saturation theory for convolution integrals. The method to be employed is the Fourier transform method already familiar to us from Chapters 7, 10, 11. Chapter 12 deals with the more classical aspects of the method, thus treating the saturation problem in X,, and Lp, 1 I p I 2. Chapter 13 gives the extension to all X(R)-spaces by duality arguments. Furthermore, the comparison of the error of approximation corresponding to two different processes is studied together with a brief account of saturation theory for strong approximation processes on arbitrary Banach spaces.
This Part is devoted to a study of saturation theory for convolution integrals. The method to be employed is the Fourier transform method already familiar to us from Chapters 7, 10, 11. Chapter 12 deals with the more classical aspects of the method, thus treating the saturation problem in X,, and Lp, 1 I p I 2. Chapter 13 gives the extension to all X(R)-spaces by duality arguments. Furthermore, the comparison of the error of approximation corresponding to two different processes is studied together with a brief account of saturation theory for strong approximation processes on arbitrary Banach spaces.