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不等式
該商品所屬分類:自然科學 -> 數學
【市場價】
553-803
【優惠價】
346-502
【介質】 book
【ISBN】9787510042829
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內容介紹



  • 出版社:世界圖書出版公司
  • ISBN:9787510042829
  • 作者:(英)加林
  • 頁數:335
  • 出版日期:2012-03-01
  • 印刷日期:2012-03-01
  • 包裝:平裝
  • 開本:16開
  • 版次:1
  • 印次:1
  • 《不等式》本書旨在介紹大量運用於線性分析中的不等式,並且詳細介紹它們的具體應用。本書以柯西不等式開頭,grothendieck不等式結束,中間用許多不等式串成一個完整的篇幅,如,loomiswhitney不等式、*大值不等式、hardy 和 hilbert不等式、超收縮和拉格朗日索伯列夫不等、beckner以及等等。這些不等式可以用來研究函數空間的性質,它們之間的線性算子,以及**和算子。書中擁有許多完整和標準的結果,提供了許多應用,如勒貝格分解定理和勒貝格密度定理、希爾伯特變換和其他奇異積分算子、鞅收斂定理、特征值分布、lidskii積公式、mercer定理和littlewood 4/3定理。本書由(英)加林著。
  • Introduction
    1 Measure and integral
    1.1 Measure
    1.2 Measurable functions
    1.3 Integration
    1.4 Notes and remarks
    2 The Cauchy-Schwarz inequality
    2.1 Cauchy's inequality
    2.2 Inner-product spaces
    2.3 The Cauchy-Schwarz inequality
    2.4 Notes and remarks
    3 The AM-GM inequality
    3.1 The AM-GM inequality
    3.2 Applications
    3.3 Notes and remarks
    4 Convexity and Jensen's inequality
    4.1 Convex sets and convex functions
    4.2 Convex functions on an interval
    4.3 Directional derivatives and sublinear functionals
    4.4 The Hahn-Banach theorem
    4.5 Normed spaces, Banach spaces and Hilbert space
    4.6 The Hahn-Banach theorem for normed spaces
    4.7 Barycentres and weak integrals
    4.8 Notes and remarks
    5 The Lp spaces
    5.1 Lp spaces, and Minkowski's inequality
    5.2 The Lebesgue decomposition theorem
    5.3 The reverse Minkowski inequality
    5.4 HSlder's inequality
    5.5 The inequalities of Liapounov and Littlewood
    5.6 Duality
    5.7 The Loomis-Whitney inequali'ty
    5.8 A Sobolev inequality
    5.9 Schur's theorem and Schur's test
    5.10 Hilbert's absolute inequality
    5.11 Notes and remarks
    6 Banach function spaces
    6.1 Banach function spaces
    6.2 Function space duality
    6.3 Orlicz space
    6.4 Notes and remarks
    7 Rearrangements
    7.1 Decreasing rearrangements
    7.2 Rearrangement-invariant Banach function spaces
    7.3 Muirhead's maximal function
    7.4 Majorization
    7.5 Calder6n's interpolation theorem and its converse
    7.6 Symmetric Banach sequence spaces
    7.7 The method of transference
    7.8 Finite doubly stochastic matrices
    7.9 Schur convexity
    7.10 Notes and remarks Maximal inequalities
    8.1 The Hardy-Riesz inequality
    8.2 The Hardy-Riesz inequality
    8.3 Related inequalities
    8.4 Strong type and weak type
    8.5 Riesz weak type
    8.6 Hardy, Littlewood, and a batsman's averages
    8.7 Riesz's sunrise lemma
    8.8 Differentiation almost everywhere
    8.9 Maximal operators in higher dimensions
    8.10 The Lebesgue density theorem
    8.11 Convolution kernels
    8.12 Hedberg's inequality
    8.13 Martingales
    8.14 Doob's inequality
    8.15 The martingale convergence theorem
    8.16 Notes and remarks
    9 Complex interpolation
    9.1 Hadamard's three lines inequality
    9.2 Compatible couples and intermediate spaces
    9.3 The Riesz-Thorin interpolation theorem
    9.4 Young's inequality
    9.5 The Hausdorff-Young inequality
    9.6 Fourier type
    9.7 The generalized Clarkson inequalities
    9.8 Uniform convexity
    9.9 Notes and remarks
    10 Real interpolation
    10.1 The Marcinkiewicz interpolation theorem: I
    10.2 Lorentz spaces
    10.3 Hardy's inequality
    10.4 The scale of Lorentz spaces
    10.5 The Marcinkiewicz interpolation theorem: II
    10.6 Notes and remarks
    11 The Hilbert transform, and Hilbert's inequalities
    11.1 The conjugate Poisson kernel
    11.2 The Hilbert transform on
    11.3 The Hilbert transform on
    11.4 Hilbert's inequality for sequences
    11.5 The Hilbert transform on T
    11.6 Multipliers
    11.7 Singular integral operators
    11.8 Singular integral operators on
    11.9 Notes and remarks
    12 Khintchine's inequality
    12.1 The contraction principle
    12.2 The reflection principle, and Lavy's inequalities
    12.3 Khintchine's inequality
    12.4 The law of the iterated logarithm
    12.5 Strongly embedded subspaces
    12.6 Stable random variables
    12.7 Sub-Gaussian random variables
    12.8 Kahane's theorem and Kahane's inequality
    12.9 Notes and remarks
    13 Hypercontractive and logarithmic Sobolev inequalities
    13.1 Bonami's inequality
    13.2 Kahane's inequality revisited
    13.3 The theorem of Lataa and Oleszkiewicz
    13.4 The logarithmic Sobolev inequality on Dd
    13.5 Gaussian measure and the Hermite polynomials
    13.6 The central limit theorem
    13.7 The Gaussian hypercontractive inequality
    13.8 Correlated Gaussian random variables
    13.9 The Gaussian logarithmic Sobolev inequality
    13.10 The logarithmic Sobolev inequality in higher dimensions
    13.11 Beckner's inequality
    13.12 The Babenko-Beckner inequality
    13.13 Notes and remarks
    14 Hadamard's inequality
    14.1 Hadamard's inequality
    14.2 Hadamard numbers
    14.3 Error-correcting codes
    14.4 Note and remark
    15 Hilbert space operator inequalities
    15.1 Jordan normal form
    15.2 Riesz operators
    15.3 Related operators
    15.4 Compact operators
    15.5 Positive compact operators
    15.6 Compact operators between Hilbert spaces
    15.7 Singular numbers, and the Rayleigh-Ritz minimax formula
    15.8 Weyl's inequality and Horn's inequality
    15.9 Ky Fan's inequality
    15.10 Operator ideals
    15.11 The Hilbert-Schmidt class
    15.12 The trace class
    15.13 Lidskii's trace formula
    15.14 Operator ideal duality
    15.15 Notes and remarks
    16 Summing operators
    16.1 Unconditional convergence
    16.2 Absolutely summing operators
    16.3 (p, q)-summing operators
    16.4 Examples of p-summing operators
    16.5 (p, 2)-summing operators between Hilbert spaces
    16.6 Positive operators on
    16.7 Mercer's theorem
    16.8 p-summing operators between Hilbert spaces
    16.9 Pietsch's domination theorem
    16.10 Pietsch's factorization theorem
    16.11 p-summing operators between Hilbert spaces
    16.12 The Dvoretzky-Rogers theorem
    16.13 Operators that factor through a Hilbert space
    16.14 Notes and remarks
    17 Approximation numbers and eigenvalues
    17.1 The approximation, Gelfand and Weyl numbers
    17.2 Subadditive and submultiplicative properties
    17.3 Pietsch's inequality
    17.4 Eigenvalues of p-summing and (p, 2)-summing endomorphisms
    17.5 Notes and remarks
    18 Grothendieck's inequality, type and cotype
    18.1 Littlewood's 4/3 inequality
    18.2 Grothendieck's inequality
    18.3 Grothendieck's theorem
    18.4 Another proof, using Paley's inequality
    18.5 The little Grothendieck theorem
    18.6 Type and cotype
    18.7 Gaussian type and cotype
    18.8 Type and cotype of LP spaces
    18.9 The little Grothendieck theorem revisited
    18.10 More on cotype
    18.11 Notes and remarks
    References
    Index of inequalities
    Index
 
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