The Resource Bochner-Riesz means on euclidean spaces, Shanzhen Lu, Dunyan Yan

Bochner-Riesz means on euclidean spaces, Shanzhen Lu, Dunyan Yan

Label
Bochner-Riesz means on euclidean spaces
Title
Bochner-Riesz means on euclidean spaces
Statement of responsibility
Shanzhen Lu, Dunyan Yan
Creator
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
This book mainly deals with the Bochner-Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner-Riesz means and important achievements attained in the last 50 years. For the Bochner-Riesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the Disc multiplier conjecture, the famous Carleson-Sjölin theorem, and Carbery-Rubio de Francia-Vega's work on almost everywhere convergence of the Bochner-Riesz means below the critical index. For the Bochner-Riesz means o
Cataloging source
MiAaPQ
http://library.link/vocab/creatorDate
1939-
http://library.link/vocab/creatorName
Lu, Shanzhen
Dewey number
515.2433
Index
index present
Language note
English
LC call number
QA404
LC item number
.L8 2013
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Yan, Dunyan
http://library.link/vocab/subjectName
  • Fourier series
  • Euclidean algorithm
Label
Bochner-Riesz means on euclidean spaces, Shanzhen Lu, Dunyan Yan
Instantiates
Publication
Note
  • Description based upon print version of record
  • Gale Virtual Reference Library
  • GVRL
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
  • Contents; Preface; 1 An introduction to multiple Fourier series; 1.1 Basic properties of multiple Fourier series; 1.2 Poisson summation formula; 1.3 Convergence and the opposite results; 1.4 Linear summation; 2 Bochner-Riesz means of multiple Fourier integral; 2.1 Localization principle and classic results on fixed-point convergence; 2.2 Lp-convergence; 2.3 Some basic facts on multipliers; 2.4 The disc conjecture and Fefferman theorem; 2.5 The Lp-boundedness of Bochner-Riesz operator Tα with α > 0; 2.6 Oscillatory integral and proof of Carleson-Sjolin theorem; 2.6.1 Oscillatory integrals
  • 2.6.2 Proof of Carleson-Sjolin theorem2.7 Kakeya maximal function; 2.8 The restriction theorem of the Fourier transform; 2.9 The case of radial functions; 2.10 Almost everywhere convergence; 2.11 Commutator of Bochner-Riesz operator; 3 Bochner-Riesz means of multiple Fourier series; 3.1 The case of being over the critical index; 3.1.1 Bochner formula; 3.1.2 The localization theorem; 3.1.3 The maximal operator Sα*; 3.2 The case of the critical index (general discussion); 3.2.1 Localization problems; 3.2.2 An example of being divergent almost everywhere
  • 3.9 The saturation problem of the uniform approximation3.10 Strong summation; 4 The conjugate Fourier integral and series; 4.1 The conjugate integral and the estimate of the kernel; 4.2 Convergence of Bochner-Riesz means for conjugate Fourier integral; 4.3 The conjugate Fourier series; 4.4 Kernel of Bochner-Riesz means of conjugate Fourier series; 4.5 The maximal operator of the conjugate partial sum; 4.6 The relations between the conjugate series and integral; 4.7 Convergence of Bochner-Riesz means of conjugate Fourier series; 4.8 (C,1) means in the conjugate case
  • 4.9 The strong summation of the conjugate Fourier series4.10 Approximation of continuous functions; Bibliography; Index
Dimensions
unknown
Extent
1 online resource (385 p.)
Form of item
online
Isbn
9789814458771
Media category
computer
Media type code
  • c
Specific material designation
remote
System control number
  • (CKB)2550000001114719
  • (EBL)1389092
  • (OCoLC)858763098
  • (SSID)ssj0001153693
  • (PQKBManifestationID)11667630
  • (PQKBTitleCode)TC0001153693
  • (PQKBWorkID)11169896
  • (PQKB)10130721
  • (MiAaPQ)EBC1389092
  • (WSP)00008745
  • (EXLCZ)992550000001114719
Label
Bochner-Riesz means on euclidean spaces, Shanzhen Lu, Dunyan Yan
Publication
Note
  • Description based upon print version of record
  • Gale Virtual Reference Library
  • GVRL
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
  • Contents; Preface; 1 An introduction to multiple Fourier series; 1.1 Basic properties of multiple Fourier series; 1.2 Poisson summation formula; 1.3 Convergence and the opposite results; 1.4 Linear summation; 2 Bochner-Riesz means of multiple Fourier integral; 2.1 Localization principle and classic results on fixed-point convergence; 2.2 Lp-convergence; 2.3 Some basic facts on multipliers; 2.4 The disc conjecture and Fefferman theorem; 2.5 The Lp-boundedness of Bochner-Riesz operator Tα with α > 0; 2.6 Oscillatory integral and proof of Carleson-Sjolin theorem; 2.6.1 Oscillatory integrals
  • 2.6.2 Proof of Carleson-Sjolin theorem2.7 Kakeya maximal function; 2.8 The restriction theorem of the Fourier transform; 2.9 The case of radial functions; 2.10 Almost everywhere convergence; 2.11 Commutator of Bochner-Riesz operator; 3 Bochner-Riesz means of multiple Fourier series; 3.1 The case of being over the critical index; 3.1.1 Bochner formula; 3.1.2 The localization theorem; 3.1.3 The maximal operator Sα*; 3.2 The case of the critical index (general discussion); 3.2.1 Localization problems; 3.2.2 An example of being divergent almost everywhere
  • 3.9 The saturation problem of the uniform approximation3.10 Strong summation; 4 The conjugate Fourier integral and series; 4.1 The conjugate integral and the estimate of the kernel; 4.2 Convergence of Bochner-Riesz means for conjugate Fourier integral; 4.3 The conjugate Fourier series; 4.4 Kernel of Bochner-Riesz means of conjugate Fourier series; 4.5 The maximal operator of the conjugate partial sum; 4.6 The relations between the conjugate series and integral; 4.7 Convergence of Bochner-Riesz means of conjugate Fourier series; 4.8 (C,1) means in the conjugate case
  • 4.9 The strong summation of the conjugate Fourier series4.10 Approximation of continuous functions; Bibliography; Index
Dimensions
unknown
Extent
1 online resource (385 p.)
Form of item
online
Isbn
9789814458771
Media category
computer
Media type code
  • c
Specific material designation
remote
System control number
  • (CKB)2550000001114719
  • (EBL)1389092
  • (OCoLC)858763098
  • (SSID)ssj0001153693
  • (PQKBManifestationID)11667630
  • (PQKBTitleCode)TC0001153693
  • (PQKBWorkID)11169896
  • (PQKB)10130721
  • (MiAaPQ)EBC1389092
  • (WSP)00008745
  • (EXLCZ)992550000001114719

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