Approximation Problems in Analysis and Probability

Weierstrass-Stone Theorem and Generalisations - A Brief Survey. Weierstrass-Stone Theorem. Closure of a Module - The Weighted Approximation Problem. Criteria of Localisability. A Differentiable Variant of the Stone-Weierstrass Theorem. Further Differentiable Variants of the Stone-Weierstrass Theorem. Strong Approximation in Finite-Dimensional Spaces. H. Whitney's Theorem on Analytic Approximation. C^∞- Approximation in a Finite-Dimensional Space. Strong Approximation in Infinite-Dimensional Spaces. Kurzweil's Theorems on Analytic Approximation. Smoothness Properties of Norms in L^p-Spaces. C^∞-Partitions of Unity in Hilbert Space. Theorem of Bonic and Frampton. Smale's Theorem. Theorem of Eells and McAlpin. Contributions of J. Wells and K. Sundaresan. Theorems of Desolneux-Moulis. C^k-Approximation of C^k by C^∞ - A Theorem of Heble. Connection Between Strong Approximation and Earlier Ideas of Bernstein-Nachbin. Strong Approximation - Other Directions. Approximation Problems in Probability. Bernstein's Proof of Weierstrass' Theorem. Some Recent Bernstein-Type Approximation Results. A Theorem of H. Steinhaus. The Wiener Process or Brownian Motion. Jump Processes - A Theorem of Skorokhod. Appendices: 1. Topological Vector Spaces. 2. Differential Calculus in Banach Spaces. 3. Differentiable Banach Manifolds. 4. Probability Theory. Bibliography. Index.