Intended for a wide range of readers, this book covers the main ideas of convex analysis and approximation theory. The author discusses the sources of these two trends in mathematical analysis, develops the main concepts and results, and mentions some beautiful theorems. The relationship of convex analysis to optimization problems, to the calculus of variations, to optimal control and to geometry is considered, and the evolution of the ideas underlying approximation theory, from its origins to the present day, is discussed. The book is addressed both to students who want to acquaint...

The creative work of Andrei N. Kolmogorov is exceptionally wide-ranging. In his studies on trigonometric and orthogonal series, the theory of measure and inte-gral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in- formation theory, he solved many conceptual and fundamental problems and posed new questions which gave rise to a great deal of further research. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence....