Methods of Approximation Theory

Regarded as a result of the activity of many mathematicians of the 20th century in the field of classical Fourier series and the theory of approximation of periodic functions, the key point of this monograph is the classification of periodic functions and developed methods that enable one to solve traditional problems of approximation theory.

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The key point of the monograph is the classification of periodic functions introduced by the author and developed methods that enable one to solve, within the framework of a common approach, traditional problems of approximation theory for large collections of periodic functions. The main results are fairly complete and are presented in the form of either exact or asymptotically exact equalities. The present monograph is, in many respects, a store of knowledge accumulated in approximation theory by the beginning of the third millennium and serving for its further development.