Analysis I: Integral Representations And Asymptotic Methods (encyclopaedia Of Mathematical Sciences)

The major achievements of mathematical analysis from Newton and Euler to modern applications of mathematics in physical sciences, engineering and other areas are presented in this volume. Its three parts cover the methods of analysis: representation methods, asymptotic methods and transform methods. The authors - the well-known analysts M.A. Evgrafov and M.V. Fedoryuk - have not simply presented a compendium of techniques but have stressed throughout the underlying unity of the various methods. The fundamental ideas are clearly presented and illustrated with interesting and non-trivial examples. References, together with guides to the literature, are provided for those readers who wish to go further. Intended for a wide range of readers, this book covers the main ideas of convex analysis and approximation theory. It discusses the sources of these trends in mathematical analysis, develops the concepts and results, and mentions some theorems. It is suitable for students and lecturers in mathematical analysis, optimization and numerical methods. v. 1. Integral representations and asymptotic methods v. 2. Convex analysis and approximation theory v. 3. Spaces of differentiable functions / S.M. Nikolʹskiĭ, ed.