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140122 ||| eng |
| 020 |
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|a 9783642657115
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| 100 |
1 |
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|a Nikol'skii, S.M.
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| 245 |
0 |
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|a Approximation of Functions of Several Variables and Imbedding Theorems
|h Elektronische Ressource
|c by S.M. Nikol'skii
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| 250 |
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|a 1st ed. 1975
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 1975, 1975
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| 300 |
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|a VIII, 420 p
|b online resource
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| 505 |
0 |
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|a 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 BasicProperties 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
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| 505 |
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|a 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 --
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| 505 |
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|a 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 of0) over Functions of Exponential Type --
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| 653 |
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|a Numerical Analysis
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| 653 |
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|a Numerical analysis
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
0 |
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|a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
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| 028 |
5 |
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|a 10.1007/978-3-642-65711-5
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-642-65711-5?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 518
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