5. APPROXIMATION BY FOURIER SUMS IN SPACES C AND L₁

Kapitel in diesem Buch

1. i-iv i
2. Contents v
3. PREFACE xi
4. PART I
5. 1. REGULARITY OF LINEAR METHODS OF SUMMATION OF FOURIER SERIES 1
6. 2. SATURATION OF LINEAR METHODS 79
7. 3. CLASSES OF PERIODIC FUNCTIONS 101
8. 4. INTEGRAL REPRESENTATIONS OF DEVIATIONS OF POLYNOMIALS GENERATED BY LINEAR PROCESSES OF SUMMATION OF FOURIER SERIES 165
9. 5. APPROXIMATION BY FOURIER SUMS IN SPACES C AND L₁ 187
10. BIBLIOGRAPHICAL NOTES (PART I) 393
11. REFERENCES (PART I) 399
12. PART II
13. 6. CONVERGENCE RATE OF FOURIER SERIES AND THE BEST APPROXIMATIONS IN THE SPACES L_p 429
14. 7. BEST APPROXIMATIONS IN THE SPACES C AND L 489
15. 8. INTERPOLATION 553
16. 9. APPROXIMATIONS IN THE SPACES OF LOCALLY SUMMABLE FUNCTIONS 597
17. 10. APPROXIMATION OF CAUCHY-TYPE INTEGRALS 679
18. 11. APPROXIMATIONS IN THE SPACES S^p 741
19. 12. APPROXIMATIONS BY ZYGMUND AND DE LA VALLÉE POUSSIN SUMS 847
20. BIBLIOGRAPHICAL NOTES (PART II) 881
21. REFERENCES (PART II) 885
22. Index 917