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＜E-Book＞
Classification and Approximation of Periodic Functions / by A.I. Stepanets
(Mathematics and Its Applications ; 333)

Edition	1st ed. 1995.
Publisher	Dordrecht : Springer Netherlands : Imprint: Springer
Year	1995
Language	English
Size	X, 366 p : online resource
Authors	*Stepanets, A.I author SpringerLink (Online service)
Subjects	LCSH:Sequences (Mathematics) LCSH:Approximation theory LCSH:Fourier analysis LCSH:Harmonic analysis FREE:Sequences, Series, Summability FREE:Approximations and Expansions FREE:Fourier Analysis FREE:Abstract Harmonic Analysis
Notes	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. 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 -- 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 HTTP:URL=https://doi.org/10.1007/978-94-011-0115-8

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