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This is an exposition of some special results on analytic or C∞ -approximation of functions in the strong sense, in finite- and infinite-dimensional spaces. It starts with H. Whitney's theorem on strong approximation by analytic functions in finite-dimensional spaces and ends with some recent results by the author on strong C∞ -approximation of functions defined in a separable Hilbert space. The volume also contains some special results on approximation of stochastic processes. The results explained in the book have been obtained over a span of nearly five decades.

Approximation, théorie de l'. --- Analyse mathématique. --- Probabilités. --- Approximation theory. --- Mathematical analysis. --- Probabilities. --- Théorie de l'approximation --- Analyse mathématique --- Probabilités --- Approximation theory --- Mathematical analysis --- Probabilities --- 517.518.8 --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Advanced calculus --- Analysis (Mathematics) --- Algebra --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Approximation of functions by polynomials and their generalizations --- 517.518.8 Approximation of functions by polynomials and their generalizations --- 517.1 Mathematical analysis --- 517.1. --- 517.1