Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorDoetsch, Gustav. author
TitleApproximation of Functions of Several Variables and Imbedding Theorems [electronic resource] / by Sergei Mihailovic Nikol'skii
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1975
Connect tohttp://dx.doi.org/10.1007/978-3-642-65711-5
Descript VIII, 420 p. online resource

CONTENT

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. AรผDroximation 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 Vallรฉe Poussin Sums -- 8.9. Representation of Functions of the Classes Bp?r in Terms of de la Vallรฉe 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


Mathematics Numerical analysis Mathematics Numerical Analysis



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram