Methods of approximation theory / A.I. Stepanets.

Includes bibliographical references (pages 393-428 and 881-916) and index.

Print version record.

PREFACE; 1. REGULARITY OF LINEAR METHODS OF SUMMATION OF FOURIER SERIES; 2. SATURATION OF LINEAR METHODS; 3. CLASSES OF PERIODIC FUNCTIONS; 4. INTEGRAL REPRESENTATIONS OF DEVIATIONS OF POLYNOMIALS GENERATED BY LINEAR PROCESSES OF SUMMATION OF FOURIER SERIES; 5. APPROXIMATION BY FOURIER SUMS IN SPACES C AND L1; BIBLIOGRAPHICAL NOTES (Part I); REFERENCES (Part I); 6. CONVERGENCE RATE OF FOURIER SERIES AND THE BEST APPROXIMATIONS IN THE SPACES Lp; 7. BEST APPROXIMATIONS IN THE SPACES C AND L; 8. INTERPOLATION; 9. APPROXIMATIONS IN THE SPACES OF LOCALLY SUMMABLE FUNCTIONS.

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.

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