Classification and Approximation of Periodic Functions
Main Author:  

Format:  eBook 
Language:  English 
Published: 
Dordrecht
Springer Netherlands
1995, 1995

Edition:  1st ed. 1995 
Series:  Mathematics and Its Applications

Subjects:  
Online Access:  
Collection:  Springer Book Archives 2004  Collection details see MPG.ReNa 
Table of Contents:
 5. Moduli of HalfDecay of Convex Functions
 6. Asymptotic Representations for ?n(f; x) on the Sets
 7. Asymptotic Equalities for and
 8. Approximations of Analytic Functions by Fourier Sums in the Uniform Metric
 9. Approximations of Entire Functions by Fourier Sums in the Uniform Metric
 10. Asymptotic Equalities for and
 11. Asymptotic Equalities for and
 12. Asymptotic Equalities for and
 13. Approximations of Analytic Functions in the Metric of the Space L
 14. Asymptotic Equalities for and
 15. Behavior of a Sequence of Partial Fourier Sums near Their Points of Divergence
 4. Simultaneous Approximation of Functions and their Derivatives by Fourier Sums
 1. Statement of the Problem and Auxiliary Facts
 2. Asymptotic Equalities for
 3. Asymptotic Equalities for
 4. Corollaries of Theorems 2.1 and 3.1
 5.Convergence Rate of the Group of Deviations
 6. Strong Summability of Fourier Series
 1. Classes of Periodic Functions
 1. Sets of Summable Functions. Moduli of Continuity
 2. The Classes H?[a, b] and H?
 3. Moduli of Continuity in the Spaces Lp. The Classes H?p
 4. Classes of Differentiable Functions
 5. Conjugate Functions and Their Classes
 6. WeilNagy Classes
 7. The Classes
 8. The Classes
 9. The Classes 35 10. Order Relation for (?, ? )Derivatives
 2. Integral Representations of Deviations of Linear Means Of Fourier Series
 1. Fourier Sums
 2. Linear Methods of Summation of Fourier Series. General Aspects
 3. Integral Representations of ?n(f;x;?)
 4. Representations of Deviations of Fourier Sums on the Sets and
 5. Representations of Deviations of Fourier Sums on the Sets and
 3. Approximations by Fourier Sums in the Spaces c and l1
 1. Simplest Extremal Problems in the Space C
 2. Simplest Extremal Problems in the Space L1
 3. Asymptotic Equalities for ? n(H?)
 4. Asymptotic Equalities for
 5. Convergence Rate of Fourier Series and Best Approximations in the Spaces lp
 1. Approximations in the Space L2
 2. Jackson Inequalities in the Space L2
 3. Multiplicators. Marcinkiewicz Theorem. Riesz Theorem. Hardy — Littlewood Theorem
 4. Imbedding Theorems for the Sets
 5. Approximations of Functions from the Sets
 6. Best Approximations of Infinitely Differentiable Functions
 7. Jackson Inequalities in the Spaces C and Lp
 6. Best Approximations in the Spaces C and l
 1. Zeros of Trigonometric Polynomials
 2. Chebyshev Theorem and de la Vallée Poussin Theorem
 3. Polynomial of Best Approximation in the Space L
 4. Approximation of Classes of Convolutions
 5. Orders of Best Approximations
 6. Exact Values of Upper Bounds of Best Approximations
 Bibliographical Notes
 References