Untitled - Cdm.unimo.it

viii Polynomial Approximation of Differential Equations
3.4 Gauss integration formulas 47
3.5 Gauss-Lobatto integration formulas 51
3.6 Gauss-Radau integration formulas 54
3.7 Clenshaw-Curtis integration formulas 55
3.8 Discrete norms 56
3.9 Discrete maximum norms 60
3.10 Scaled weights 62
4. Transforms
4.1 Fourier transforms 65
4.2 Aliasing 68
4.3 Fast Fourier transform 70
4.4 Other fast methods 76
5. Functional spaces
5.1 The Lebesgue integral 77
5.2 Spaces of measurable functions 81
5.3 Completeness 82
5.4 Weak derivatives 84
5.5 Transformation of measurable functions in R 85
5.6 Sobolev spaces in R 87
5.7 Sobolev spaces in intervals 90
6. Results in approximation theory
6.1 The problem of best approximation 93
6.2 Estimates for the projection operator 96
6.3 Inverse inequalities 104
6.4 Other projection operators 107
6.5 Convergence of the Gaussian formulas 111
6.6 Estimates for the interpolation operator 115
6.7 Laguerre and Hermite functions 119
6.8 Refinements 123