Functional Analysis : : Introduction to Further Topics in Analysis / / Rami Shakarchi, Elias M. Stein.
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, an...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2011] ©2012 |
Year of Publication: | 2011 |
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Stein, Elias M., author. aut http://id.loc.gov/vocabulary/relators/aut Functional Analysis : Introduction to Further Topics in Analysis / Rami Shakarchi, Elias M. Stein. Princeton, NJ : Princeton University Press, [2011] ©2012 1 online resource (448 p.) : 27 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- Foreword -- Contents -- Preface to Book IV -- 1. Lp Spaces and Banach Spaces -- 2. Lp Spaces in Harmonic Analysis -- 3. Distributions: Generalized Functions -- 4. Applications of the Baire Category Theorem -- 5. Rudiments of Probability Theory -- 6. An Introduction to Brownian Motion -- 7. A Glimpse into Several Complex Variables -- 8. Oscillatory Integrals in Fourier Analysis -- Notes and References -- Bibliography -- Symbol Glossary -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) MATHEMATICS / Functional Analysis. bisacsh Shakarchi, Rami, author. aut http://id.loc.gov/vocabulary/relators/aut Shakarchi, Rami, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Stein, Elias M., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691113876 https://doi.org/10.1515/9781400840557?locatt=mode:legacy https://www.degruyter.com/isbn/9781400840557 Cover https://www.degruyter.com/cover/covers/9781400840557.jpg |
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author |
Stein, Elias M., Stein, Elias M., Shakarchi, Rami, |
spellingShingle |
Stein, Elias M., Stein, Elias M., Shakarchi, Rami, Functional Analysis : Introduction to Further Topics in Analysis / Frontmatter -- Foreword -- Contents -- Preface to Book IV -- 1. Lp Spaces and Banach Spaces -- 2. Lp Spaces in Harmonic Analysis -- 3. Distributions: Generalized Functions -- 4. Applications of the Baire Category Theorem -- 5. Rudiments of Probability Theory -- 6. An Introduction to Brownian Motion -- 7. A Glimpse into Several Complex Variables -- 8. Oscillatory Integrals in Fourier Analysis -- Notes and References -- Bibliography -- Symbol Glossary -- Index |
author_facet |
Stein, Elias M., Stein, Elias M., Shakarchi, Rami, Shakarchi, Rami, Shakarchi, Rami, Shakarchi, Rami, Shakarchi, Rami, Stein, Elias M., Stein, Elias M., |
author_variant |
e m s em ems e m s em ems r s rs |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Shakarchi, Rami, Shakarchi, Rami, Shakarchi, Rami, Shakarchi, Rami, Stein, Elias M., Stein, Elias M., |
author2_variant |
r s rs r s rs r s rs e m s em ems e m s em ems |
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VerfasserIn VerfasserIn MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR |
author_sort |
Stein, Elias M., |
title |
Functional Analysis : Introduction to Further Topics in Analysis / |
title_sub |
Introduction to Further Topics in Analysis / |
title_full |
Functional Analysis : Introduction to Further Topics in Analysis / Rami Shakarchi, Elias M. Stein. |
title_fullStr |
Functional Analysis : Introduction to Further Topics in Analysis / Rami Shakarchi, Elias M. Stein. |
title_full_unstemmed |
Functional Analysis : Introduction to Further Topics in Analysis / Rami Shakarchi, Elias M. Stein. |
title_auth |
Functional Analysis : Introduction to Further Topics in Analysis / |
title_alt |
Frontmatter -- Foreword -- Contents -- Preface to Book IV -- 1. Lp Spaces and Banach Spaces -- 2. Lp Spaces in Harmonic Analysis -- 3. Distributions: Generalized Functions -- 4. Applications of the Baire Category Theorem -- 5. Rudiments of Probability Theory -- 6. An Introduction to Brownian Motion -- 7. A Glimpse into Several Complex Variables -- 8. Oscillatory Integrals in Fourier Analysis -- Notes and References -- Bibliography -- Symbol Glossary -- Index |
title_new |
Functional Analysis : |
title_sort |
functional analysis : introduction to further topics in analysis / |
publisher |
Princeton University Press, |
publishDate |
2011 |
physical |
1 online resource (448 p.) : 27 line illus. Issued also in print. |
contents |
Frontmatter -- Foreword -- Contents -- Preface to Book IV -- 1. Lp Spaces and Banach Spaces -- 2. Lp Spaces in Harmonic Analysis -- 3. Distributions: Generalized Functions -- 4. Applications of the Baire Category Theorem -- 5. Rudiments of Probability Theory -- 6. An Introduction to Brownian Motion -- 7. A Glimpse into Several Complex Variables -- 8. Oscillatory Integrals in Fourier Analysis -- Notes and References -- Bibliography -- Symbol Glossary -- Index |
isbn |
9781400840557 9783110442502 9780691113876 |
url |
https://doi.org/10.1515/9781400840557?locatt=mode:legacy https://www.degruyter.com/isbn/9781400840557 https://www.degruyter.com/cover/covers/9781400840557.jpg |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.7 |
dewey-sort |
3515.7 |
dewey-raw |
515.7 |
dewey-search |
515.7 |
doi_str_mv |
10.1515/9781400840557?locatt=mode:legacy |
oclc_num |
753980218 |
work_keys_str_mv |
AT steineliasm functionalanalysisintroductiontofurthertopicsinanalysis AT shakarchirami functionalanalysisintroductiontofurthertopicsinanalysis |
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ids_txt_mv |
(DE-B1597)528150 (OCoLC)753980218 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
is_hierarchy_title |
Functional Analysis : Introduction to Further Topics in Analysis / |
container_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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