Author | Butzer, Paul P. author |
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Title | Semi-Groups of Operators and Approximation [electronic resource] / by Paul P. Butzer, Hubert Berens |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1967 |
Connect to | http://dx.doi.org/10.1007/978-3-642-46066-1 |
Descript | XII, 322 p. online resource |
One Fundamentals of Semi-Group Theory -- 1.0 Introduction -- 1.1 Elements of Semi-Group Theory -- 1.2 Representation Theorems for Semi-Groups of Operators -- 1.3 Resolvent and Characterization of the Generator -- 1.4 Dual Semi-Groups -- 1.5 Trigonometric Semi-Groups -- 1.6 Notes and Remarks -- Two Approximation Theorems for Semi-Groups of Operators -- 2.0 Introduction -- 2.1 Favard Classes and the Fundamental Approximation Theorems -- 2.2 Taylor, Peano, and Riemann Operators Generated by Semi-Groups of Operators -- 2.3 Theorems of Non-optimal Approximation -- 2.4 Applications to Periodic Singular Integrals -- 2.5 Approximation Theorems for Resolvent Operators -- 2.6 Laplace Transforms in Connection with a Generalized Heat Equation -- 2.7 Notes and Remarks -- Three Intermediate Spaces and Semi-Groups -- 3.0 Scope of the Chapter -- 3.1 Banach Subspaces of X Generated by Semi-Groups of Operators -- 3.2 Intermediate Spaces and Interpolation -- 3.3 Lorentz Spaces and Convexity Theorems -- 3.4 Intermediate Spaces of X and D(Ar) -- 3.5 Equivalent Characterizations of X?, r; q Generated by Holomorphic Semi-Groups -- 3.6 Notes and Remarks -- Four Applications to Singular Integrals -- 4.0 Orientation -- 4.1 Periodic Functions -- 4.2 The Hilbert Transform and the Cauchy-Poisson Singular Integral -- 4.3 The Weierstrass Integral on Euclidean n-Space -- 4.4 Notes and Remarks