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Classification and Approximation of Periodic Functions

Bibliographic Details
Main Author: Stepanets, A.I.
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1995, 1995
Edition:1st ed. 1995
Series:Mathematics and Its Applications
Subjects:
Harmonic Analysis
Fourier Analysis
Approximations And Expansions
Sequences, Series, Summability
Abstract Harmonic Analysis
Sequences (mathematics)
Approximation Theory
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 5. Moduli of Half-Decay 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. Weil-Nagy 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

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