The Resource Functional analysis : introduction to further topics in analysis, Elias M. Stein, Rami Shakarchi
Functional analysis : introduction to further topics in analysis, Elias M. Stein, Rami Shakarchi
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 Summary

 "This is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. Beginning with the basic facts of functional analysis, this volume looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. The authors then use the Baire category theorem to illustrate several points, including the existence of Besicovitch sets. The second half of the book introduces readers to other central topics in analysis, such as probability theory and Brownian motion, which culminates in the solution of Dirichlet's problem. The concluding chapters explore several complex variables and oscillatory integrals in Fourier analysis, and illustrate applications to such diverse areas as nonlinear dispersion equations and the problem of counting lattice points. Throughout the book, the authors focus on key results in each area and stress the organic unity of the subject. A comprehensive and authoritative text that treats some of the main topics of modern analysis A look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables Key results in each area discussed in relation to other areas of mathematics Highlights the organic unity of large areas of analysis traditionally split into subfields Interesting exercises and problems illustrate ideas Clear proofs provided "
 "This book covers such topics as L̂p spaces, distributions, Baire category, probability theory and Brownian motion, several complex variables and oscillatory integrals in Fourier analysis. The authors focus on key results in each area, highlighting their importance and the organic unity of the subject"
 Language
 eng
 Extent
 1 online resource (xv, 423 pages)
 Contents

 Cover; Contents; Foreword; Preface; Chapter 1. L[sup(p)] Spaces and Banach Spaces; 1 L[sup(p)] spaces; 1.1 The Hölder and Minkowski inequalities; 1.2 Completeness of L[sup(p)]; 1.3 Further remarks; 2 The case p = ∞; 3 Banach spaces; 3.1 Examples; 3.2 Linear functionals and the dual of a Banach space; 4 The dual space of L[sup(p)] when 1 ≤ p < ∞; 5 More about linear functionals; 5.1 Separation of convex sets; 5.2 The HahnBanach Theorem; 5.3 Some consequences; 5.4 The problem of measure; 6 Complex L[sup(p)] and Banach spaces; 7 Appendix: The dual of C(X)
 7.1 The case of positive linear functionals7.2 The main result; 7.3 An extension; 8 Exercises; 9 Problems; Chapter 2. L[sup(p)] Spaces in Harmonic Analysis; 1 Early Motivations; 2 The Riesz interpolation theorem; 2.1 Some examples; 3 The L[sup(p) theory of the Hilbert transform; 3.1 The L[sup(2)] formalism; 3.2 The L[sup(p) theorem; 3.3 Proof of Theorem 3.2; 4 The maximal function and weaktype estimates; 4.1 The L[sup(p)] inequality; 5 The Hardy space H[sup(1)][sub(r); 5.1 Atomic decomposition of H[sup(1)[sub(r); 5.2 An alternative definition of H[sup(1)[sub(r)]
 5.3 Application to the Hilbert transform6 The space H[sup(1)[sub(r)] and maximal functions; 6.1 The space BMO; 7 Exercises; 8 Problems; Chapter 3. Distributions: Generalized Functions; 1 Elementary properties; 1.1 Definitions; 1.2 Operations on distributions; 1.3 Supports of distributions; 1.4 Tempered distributions; 1.5 Fourier transform; 1.6 Distributions with point supports; 2 Important examples of distributions; 2.1 The Hilbert transform and pv(1/x); 2.2 Homogeneous distributions; 2.3 Fundamental solutions
 2.4 Fundamental solution to general partial differential equations with constant coefficients2.5 Parametrices and regularity for elliptic equations; 3 CaldeórnZygmund distributions and L[sup(p)] estimates; 3.1 Defining properties; 3.2 The L[sup(p) theory; 4 Exercises; 5 Problems; Chapter 4. Applications of the Baire Category Theorem; 1 The Baire category theorem; 1.1 Continuity of the limit of a sequence of continuous functions; 1.2 Continuous functions that are nowhere differentiable; 2 The uniform boundedness principle; 2.1 Divergence of Fourier series; 3 The open mapping theorem
 3.1 Decay of Fourier coefficients of L[sup(1)]functions4 The closed graph theorem; 4.1 Grothendieck's theorem on closed subspaces of L[sup(p)]; 5 Besicovitch sets; 6 Exercises; 7 Problems; Chapter 5. Rudiments of Probability Theory; 1 Bernoulli trials; 1.1 Coin flips; 1.2 The case N = ∞; 1.3 Behavior of S[sub(N)] as N → ∞, first resultes; 1.4 Central limit theorem; 1.5 Statement and proof of the theorem; 1.6 Random series; 1.7 Random Fourier series; 1.8 Bernoulli trials; 2 Sums of independent random variables; 2.1 Law of large numbers and ergodic theorem; 2.2 The role of martingales
 Isbn
 9781400840557
 Label
 Functional analysis : introduction to further topics in analysis
 Title
 Functional analysis
 Title remainder
 introduction to further topics in analysis
 Statement of responsibility
 Elias M. Stein, Rami Shakarchi
 Language
 eng
 Summary

 "This is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. Beginning with the basic facts of functional analysis, this volume looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. The authors then use the Baire category theorem to illustrate several points, including the existence of Besicovitch sets. The second half of the book introduces readers to other central topics in analysis, such as probability theory and Brownian motion, which culminates in the solution of Dirichlet's problem. The concluding chapters explore several complex variables and oscillatory integrals in Fourier analysis, and illustrate applications to such diverse areas as nonlinear dispersion equations and the problem of counting lattice points. Throughout the book, the authors focus on key results in each area and stress the organic unity of the subject. A comprehensive and authoritative text that treats some of the main topics of modern analysis A look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables Key results in each area discussed in relation to other areas of mathematics Highlights the organic unity of large areas of analysis traditionally split into subfields Interesting exercises and problems illustrate ideas Clear proofs provided "
 "This book covers such topics as L̂p spaces, distributions, Baire category, probability theory and Brownian motion, several complex variables and oscillatory integrals in Fourier analysis. The authors focus on key results in each area, highlighting their importance and the organic unity of the subject"
 Assigning source

 Provided by publisher
 Provided by publisher
 Cataloging source
 N$T
 http://library.link/vocab/creatorDate
 19312018
 http://library.link/vocab/creatorName
 Stein, Elias M.
 Index
 index present
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Shakarchi, Rami
 Series statement
 Princeton lectures in analysis
 Series volume
 4
 http://library.link/vocab/subjectName

 Functional analysis
 MATHEMATICS
 Functional analysis
 MATHEMATICS / Functional Analysis
 Label
 Functional analysis : introduction to further topics in analysis, Elias M. Stein, Rami Shakarchi
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 413416) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Cover; Contents; Foreword; Preface; Chapter 1. L[sup(p)] Spaces and Banach Spaces; 1 L[sup(p)] spaces; 1.1 The Hölder and Minkowski inequalities; 1.2 Completeness of L[sup(p)]; 1.3 Further remarks; 2 The case p = ∞; 3 Banach spaces; 3.1 Examples; 3.2 Linear functionals and the dual of a Banach space; 4 The dual space of L[sup(p)] when 1 ≤ p < ∞; 5 More about linear functionals; 5.1 Separation of convex sets; 5.2 The HahnBanach Theorem; 5.3 Some consequences; 5.4 The problem of measure; 6 Complex L[sup(p)] and Banach spaces; 7 Appendix: The dual of C(X)
 7.1 The case of positive linear functionals7.2 The main result; 7.3 An extension; 8 Exercises; 9 Problems; Chapter 2. L[sup(p)] Spaces in Harmonic Analysis; 1 Early Motivations; 2 The Riesz interpolation theorem; 2.1 Some examples; 3 The L[sup(p) theory of the Hilbert transform; 3.1 The L[sup(2)] formalism; 3.2 The L[sup(p) theorem; 3.3 Proof of Theorem 3.2; 4 The maximal function and weaktype estimates; 4.1 The L[sup(p)] inequality; 5 The Hardy space H[sup(1)][sub(r); 5.1 Atomic decomposition of H[sup(1)[sub(r); 5.2 An alternative definition of H[sup(1)[sub(r)]
 5.3 Application to the Hilbert transform6 The space H[sup(1)[sub(r)] and maximal functions; 6.1 The space BMO; 7 Exercises; 8 Problems; Chapter 3. Distributions: Generalized Functions; 1 Elementary properties; 1.1 Definitions; 1.2 Operations on distributions; 1.3 Supports of distributions; 1.4 Tempered distributions; 1.5 Fourier transform; 1.6 Distributions with point supports; 2 Important examples of distributions; 2.1 The Hilbert transform and pv(1/x); 2.2 Homogeneous distributions; 2.3 Fundamental solutions
 2.4 Fundamental solution to general partial differential equations with constant coefficients2.5 Parametrices and regularity for elliptic equations; 3 CaldeórnZygmund distributions and L[sup(p)] estimates; 3.1 Defining properties; 3.2 The L[sup(p) theory; 4 Exercises; 5 Problems; Chapter 4. Applications of the Baire Category Theorem; 1 The Baire category theorem; 1.1 Continuity of the limit of a sequence of continuous functions; 1.2 Continuous functions that are nowhere differentiable; 2 The uniform boundedness principle; 2.1 Divergence of Fourier series; 3 The open mapping theorem
 3.1 Decay of Fourier coefficients of L[sup(1)]functions4 The closed graph theorem; 4.1 Grothendieck's theorem on closed subspaces of L[sup(p)]; 5 Besicovitch sets; 6 Exercises; 7 Problems; Chapter 5. Rudiments of Probability Theory; 1 Bernoulli trials; 1.1 Coin flips; 1.2 The case N = ∞; 1.3 Behavior of S[sub(N)] as N → ∞, first resultes; 1.4 Central limit theorem; 1.5 Statement and proof of the theorem; 1.6 Random series; 1.7 Random Fourier series; 1.8 Bernoulli trials; 2 Sums of independent random variables; 2.1 Law of large numbers and ergodic theorem; 2.2 The role of martingales
 Control code
 ocn753980218
 Dimensions
 unknown
 Extent
 1 online resource (xv, 423 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9781400840557
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Note
 JSTOR
 http://library.link/vocab/ext/overdrive/overdriveId
 22573/ctvckv9sz
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)753980218
 Label
 Functional analysis : introduction to further topics in analysis, Elias M. Stein, Rami Shakarchi
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 413416) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Cover; Contents; Foreword; Preface; Chapter 1. L[sup(p)] Spaces and Banach Spaces; 1 L[sup(p)] spaces; 1.1 The Hölder and Minkowski inequalities; 1.2 Completeness of L[sup(p)]; 1.3 Further remarks; 2 The case p = ∞; 3 Banach spaces; 3.1 Examples; 3.2 Linear functionals and the dual of a Banach space; 4 The dual space of L[sup(p)] when 1 ≤ p < ∞; 5 More about linear functionals; 5.1 Separation of convex sets; 5.2 The HahnBanach Theorem; 5.3 Some consequences; 5.4 The problem of measure; 6 Complex L[sup(p)] and Banach spaces; 7 Appendix: The dual of C(X)
 7.1 The case of positive linear functionals7.2 The main result; 7.3 An extension; 8 Exercises; 9 Problems; Chapter 2. L[sup(p)] Spaces in Harmonic Analysis; 1 Early Motivations; 2 The Riesz interpolation theorem; 2.1 Some examples; 3 The L[sup(p) theory of the Hilbert transform; 3.1 The L[sup(2)] formalism; 3.2 The L[sup(p) theorem; 3.3 Proof of Theorem 3.2; 4 The maximal function and weaktype estimates; 4.1 The L[sup(p)] inequality; 5 The Hardy space H[sup(1)][sub(r); 5.1 Atomic decomposition of H[sup(1)[sub(r); 5.2 An alternative definition of H[sup(1)[sub(r)]
 5.3 Application to the Hilbert transform6 The space H[sup(1)[sub(r)] and maximal functions; 6.1 The space BMO; 7 Exercises; 8 Problems; Chapter 3. Distributions: Generalized Functions; 1 Elementary properties; 1.1 Definitions; 1.2 Operations on distributions; 1.3 Supports of distributions; 1.4 Tempered distributions; 1.5 Fourier transform; 1.6 Distributions with point supports; 2 Important examples of distributions; 2.1 The Hilbert transform and pv(1/x); 2.2 Homogeneous distributions; 2.3 Fundamental solutions
 2.4 Fundamental solution to general partial differential equations with constant coefficients2.5 Parametrices and regularity for elliptic equations; 3 CaldeórnZygmund distributions and L[sup(p)] estimates; 3.1 Defining properties; 3.2 The L[sup(p) theory; 4 Exercises; 5 Problems; Chapter 4. Applications of the Baire Category Theorem; 1 The Baire category theorem; 1.1 Continuity of the limit of a sequence of continuous functions; 1.2 Continuous functions that are nowhere differentiable; 2 The uniform boundedness principle; 2.1 Divergence of Fourier series; 3 The open mapping theorem
 3.1 Decay of Fourier coefficients of L[sup(1)]functions4 The closed graph theorem; 4.1 Grothendieck's theorem on closed subspaces of L[sup(p)]; 5 Besicovitch sets; 6 Exercises; 7 Problems; Chapter 5. Rudiments of Probability Theory; 1 Bernoulli trials; 1.1 Coin flips; 1.2 The case N = ∞; 1.3 Behavior of S[sub(N)] as N → ∞, first resultes; 1.4 Central limit theorem; 1.5 Statement and proof of the theorem; 1.6 Random series; 1.7 Random Fourier series; 1.8 Bernoulli trials; 2 Sums of independent random variables; 2.1 Law of large numbers and ergodic theorem; 2.2 The role of martingales
 Control code
 ocn753980218
 Dimensions
 unknown
 Extent
 1 online resource (xv, 423 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9781400840557
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Note
 JSTOR
 http://library.link/vocab/ext/overdrive/overdriveId
 22573/ctvckv9sz
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)753980218
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