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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

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
Creator
Contributor
Subject
Genre
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"--
Member of
Assigning source
  • Provided by publisher
  • Provided by publisher
Cataloging source
N$T
http://library.link/vocab/creatorDate
1931-2018
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
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 413-416) 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 = &#x221E;; 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 &#x2264; p < &#x221E;; 5 More about linear functionals; 5.1 Separation of convex sets; 5.2 The Hahn-Banach 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 weak-type 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 Caldeórn-Zygmund 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 = &#x221E;; 1.3 Behavior of S[sub(N)] as N &#x2192; &#x221E;, 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
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 413-416) 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 = &#x221E;; 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 &#x2264; p < &#x221E;; 5 More about linear functionals; 5.1 Separation of convex sets; 5.2 The Hahn-Banach 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 weak-type 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 Caldeórn-Zygmund 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 = &#x221E;; 1.3 Behavior of S[sub(N)] as N &#x2192; &#x221E;, 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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