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Approximation of Functions of Several Variables and Imbedding Theorems / by S.M. Nikol'skii

データ種別	電子書籍
版	1st ed. 1975.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	1975

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URL	配架場所	巻　次	請求記号	資料番号	状　態	コメント	予約	文庫区分	教員指定/教員執筆/多読	仮想書架
URL	オンライン			EB1983004

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書誌ID	OB01018992
本文言語	英語
一般注記	1. Preparatory Information -- 1.1. The Spaces C(?) and Lp(?) -- 1.2. Normed Linear Spaces -- 1.3. Properties of the Space Lp(?) -- 1.4. Averaging of Functions According to Sobolev -- 1.5. Generalized Functions -- 2. Trigonometric Polynomials -- 2.1. Theorems on Zeros. Linear Independence -- 2.2. Important Examples of Trigonometric Polynomials -- 2.3. The Trigonometric Interpolation Polynomial of Lagrange -- 2.4. The Interpolation Formula of M. Riesz -- 2.5. The Bernstein's Inequality -- 2.6. Trigonometric Polynomials of Several Variables -- 2.7. Trigonometric Polynomials Relative to Certain Variables -- 3. Entire Functions of Exponential Type, Bounded on ?n -- 3.1. Preparatory Material -- 3.2. Interpolation Formula -- 3.3. Inequalities of Different Metrics for Entire Functions of Exponential Type -- 3.4. Inequalities of Different Dimensions for Entire Functions of Exponential Type -- 3.5. Subspaces of Functions of Given Exponential Type -- 3.6. Convolutions with Entire Functions of Exponential Type -- 4. The Function Classes W, H, B -- 4.1. The Generalized Derivative -- 4.2. Finite Differences and Moduli of Continuity -- 4.3. The Classes W, H, B -- 4.4. Representation of an Intermediate Derivate in Terms of a Derivative of Higher Order and the Function. Corollaries -- 4.5. More on Sobolev Averages -- 4.6. Estimate of the Increment Relative to a Direction -- 4.7. Completeness of the Spaces W, H, B -- 4.8. Estimates of the Derivative by the Difference Quotient -- 5. Direct and Inverse Theorems of the Theory of Approximation. Equivalent Norms -- 5.1. Introduction -- 5.2. AüDroximation Theorem -- 5.3. Periodic Classes -- 5.4. Inverse Theorems of the Theory of Approximations -- 5.5. Direct and Inverse Theorems on Best Approximations. Equivalent H-Norms -- 5.6. Definition of B-Classes with the Aid of 0) over Functions of Exponential Type -- 8.8. Decomposition of a Regular Function into Series Relative to de la Vallée Poussin Sums -- 8.9. Representation of Functions of the Classes Bp?r in Terms of de la Vallée Poussin Series. Null Classes (1 ? p ? ?) -- 8.10. Series Relative to Dirichlet Sums (1 < p < ?) -- 9. The Liouville Classes L -- 9.1. Introduction -- 9.2. Definitions and Basic Properties of the Classes Lpr and pr -- 9.3. Interrelationships among Liouville and other Classes -- 9.4. Integral Representation of Anisotropic Classes -- 9.5. Imbedding Theorems -- 9.6. Imbedding Theorem with a Limiting Exponent -- 9.7. Nonequivalence of the Classes Bpr and Lpr -- Remarks -- Literature -- Index of Names. License restrictions may limit access
著者標目	*Nikol'skii, S.M SpringerLink (Online service)
統一書名標目	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
件　名	LCSH:Numerical analysis FREE:Numerical Analysis
分　類	LCC:QA297-299.4 DC23:518
巻冊次	ISBN:9783642657115 RefWorks出力（各巻） print ; ISBN:9783642657139 RefWorks出力（各巻） print ; ISBN:9783540064428 RefWorks出力（各巻） print ; ISBN:9783642657122 RefWorks出力（各巻）
資料種別	機械可読データファイル

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