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Coupled with its sequel, this book gives a connected, unified exposition of Approximation Theory for functions of one real variable. It describes spaces of functions such as Sobolev, Lipschitz, Besov rearrangement-invariant function spaces and interpolation of operators. Other topics include Weierstrauss and best approximation theorems, properties of polynomials and splines. It contains history and proofs with an emphasis on principal results.

Constructive Approximation

1. Theorems of Weierstrass.- 2. Spaces of Functions.- 3. Best Approximation.- 4. Properties of Polynomials.- 5. Splines.- 6. K-Functionals and Interpolation Spaces.- 7. Central Theorems of Approximation.- 8. Influence of Endpoints in Polynomial Approximation.- 9. Approximation by Operators.- 10. Bernstein Polynomials.- 11. Approximation of Classes of Functions, Müntz Theorems.- 12. Spline Approximation.- 13. Spline Interpolation and Projections onto Spline Spaces.