Methods Of Approximation Theory

ISBN: 9789067644273 出版年：2011 页码：940 Stepanets, Alexander I De Gruyter

This monograph can be 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, beginning with H. Lebesgue, D. Jackson, and S. N. Bernstein. 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, including, as particular cases, the well-known Weyl--Nagy and Sobolev classes as well as classes of functions defined by convolutions with arbitrary summable kernels. The developed methods enable one to solve problems of approximation theory not only in the periodic case but also in the case where objects of approximation are functions locally integrable on the entire axis and functions defined by Cauchy-type integrals in domains of the complex plane bounded by rectifiable Jordan curves. The main results are fairly complete and are presented in the form of either exact or asymptotically exact equalities. Most results of the monograph represent the latest achievements, which have not yet been published in existing monographs.