The theory of approximation of functions is one of the central branchesin mathematical analysis and has been developed over a number ofdecades. This monograph deals with a series of problems related to oneof the directions of the theory, namely, the approximation of periodicfunctions by trigonometric polynomials generated by linear methods ofsummation of Fourier series. More specific, the following linear methodsare investigated: classical methods of Fourier, Fejér, Riesz, andRoginski. For these methods the so-called Kolmogorov-Nikol'skii problemis considered, which consists of finding exact and asymptotically exactqualities for the upper bounds of deviations of polynomials generated bygiven linear methods on given classes of 2-periodic functions. Muchattention is also given to the multidimensional case.
The material presented in this monograph did not lose its importancesince the publication of the Russian edition (1981). Moreover, newmaterial has been added and several corrections were made. In this fieldof mathematics numerous deep results were obtained, many important andcomplicated problems were solved, and new methods were developed, whichcan be extremely useful for many mathematicians. All principle problemsconsidered in this monograph are given in the final form, i.e. in theform of exact asymptotic equalities, and, therefore, retain theirimportance and interest for a long time.
2001; xii+468 pages ISBN 90-6764-347-5 Price (all prices are subject to change without notice): EUR 254/US$ 363
-periodic functions. Muchattention is also given to the multidimensional case.