東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Fundamentals of fourier analysis

Grafakos, Loukas.

Linked to FindBook

Google Book

Amazon

博客來

Fundamentals of fourier analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fundamentals of fourier analysis/ by Loukas Grafakos.
Author:	Grafakos, Loukas.
Published:	Cham :Springer International Publishing : : 2024.,
Description:	xvi, 407 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Introductory Material -- 2 Fourier Transforms, Tempered Distributions, Approximate Identities -- 3 Singular Integrals -- 4 Vector-Valued Singular Integrals and Littlewood-Paley Theory -- 5 Fractional Integrability or Differentiability and Multiplier Theorems -- 6 Bounded Mean Oscillation -- 7 Hardy Spaces -- 8 Weighted Inequalities -- Historical Notes -- Appendix A Orthogonal Matrices -- Appendix B Subharmonic Functions -- Appendix C Poisson Kernel on the Unit Strip -- Appendix D Density for Subadditive Operators -- Appendix E Transposes and Adjoints of Linear Operators -- Appendix F Faa di Bruno Formula -- Appendix G Besicovitch Covering Lemma -- Glossary -- References -- Index.
Contained By:	Springer Nature eBook
Subject:	Fourier analysis. -
Online resource:	https://doi.org/10.1007/978-3-031-56500-7
ISBN:	9783031565007

Fundamentals of fourier analysis
Grafakos, Loukas.

Fundamentals of fourier analysis[electronic resource] /by Loukas Grafakos. - Cham :Springer International Publishing :2024. - xvi, 407 p. :ill., digital ;24 cm. - Graduate texts in mathematics,3022197-5612 ;. - Graduate texts in mathematics ;302..

1 Introductory Material -- 2 Fourier Transforms, Tempered Distributions, Approximate Identities -- 3 Singular Integrals -- 4 Vector-Valued Singular Integrals and Littlewood-Paley Theory -- 5 Fractional Integrability or Differentiability and Multiplier Theorems -- 6 Bounded Mean Oscillation -- 7 Hardy Spaces -- 8 Weighted Inequalities -- Historical Notes -- Appendix A Orthogonal Matrices -- Appendix B Subharmonic Functions -- Appendix C Poisson Kernel on the Unit Strip -- Appendix D Density for Subadditive Operators -- Appendix E Transposes and Adjoints of Linear Operators -- Appendix F Faa di Bruno Formula -- Appendix G Besicovitch Covering Lemma -- Glossary -- References -- Index.

This self-contained text introduces Euclidean Fourier Analysis to graduate students who have completed courses in Real Analysis and Complex Variables. It provides sufficient content for a two course sequence in Fourier Analysis or Harmonic Analysis at the graduate level. In true pedagogical spirit, each chapter presents a valuable selection of exercises with targeted hints that will assist the reader in the development of research skills. Proofs are presented with care and attention to detail. Examples are provided to enrich understanding and improve overall comprehension of the material. Carefully drawn illustrations build intuition in the proofs. Appendices contain background material for those that need to review key concepts. Compared with the author's other GTM volumes (Classical Fourier Analysis and Modern Fourier Analysis), this text offers a more classroom-friendly approach as it contains shorter sections, more refined proofs, and a wider range of exercises. Topics include the Fourier Transform, Multipliers, Singular Integrals, Littlewood-Paley Theory, BMO, Hardy Spaces, and Weighted Estimates, and can be easily covered within two semesters.

ISBN: 9783031565007

Standard No.: 10.1007/978-3-031-56500-7doiSubjects--Topical Terms:

532730
Fourier analysis.

LC Class. No.: QA403.5

Dewey Class. No.: 515.2433

Fundamentals of fourier analysis
LDR:02877nmm a2200337 a 4500 001 2374434
003 DE-He213
005 20240721125229.0
006 m d
007 cr nn 008maaau
008 241231s2024 sz s 0 eng d
020 $a 9783031565007 $q (electronic bk.)
020 $a 9783031564994 $q (paper)
024 7 $a 10.1007/978-3-031-56500-7 $2 doi
035 $a 978-3-031-56500-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA403.5
072 7 $a PBKF $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.2433 $2 23
090 $a QA403.5 $b .G736 2024
100 1 $a Grafakos, Loukas. $3 923954
245 1 0 $a Fundamentals of fourier analysis $h [electronic resource] / $c by Loukas Grafakos.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2024.
300 $a xvi, 407 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 2197-5612 ; $v 302
505 0 $a 1 Introductory Material -- 2 Fourier Transforms, Tempered Distributions, Approximate Identities -- 3 Singular Integrals -- 4 Vector-Valued Singular Integrals and Littlewood-Paley Theory -- 5 Fractional Integrability or Differentiability and Multiplier Theorems -- 6 Bounded Mean Oscillation -- 7 Hardy Spaces -- 8 Weighted Inequalities -- Historical Notes -- Appendix A Orthogonal Matrices -- Appendix B Subharmonic Functions -- Appendix C Poisson Kernel on the Unit Strip -- Appendix D Density for Subadditive Operators -- Appendix E Transposes and Adjoints of Linear Operators -- Appendix F Faa di Bruno Formula -- Appendix G Besicovitch Covering Lemma -- Glossary -- References -- Index.
520 $a This self-contained text introduces Euclidean Fourier Analysis to graduate students who have completed courses in Real Analysis and Complex Variables. It provides sufficient content for a two course sequence in Fourier Analysis or Harmonic Analysis at the graduate level. In true pedagogical spirit, each chapter presents a valuable selection of exercises with targeted hints that will assist the reader in the development of research skills. Proofs are presented with care and attention to detail. Examples are provided to enrich understanding and improve overall comprehension of the material. Carefully drawn illustrations build intuition in the proofs. Appendices contain background material for those that need to review key concepts. Compared with the author's other GTM volumes (Classical Fourier Analysis and Modern Fourier Analysis), this text offers a more classroom-friendly approach as it contains shorter sections, more refined proofs, and a wider range of exercises. Topics include the Fourier Transform, Multipliers, Singular Integrals, Littlewood-Paley Theory, BMO, Hardy Spaces, and Weighted Estimates, and can be easily covered within two semesters.
650 0 $a Fourier analysis. $3 532730
650 1 4 $a Fourier Analysis. $3 891095
650 2 4 $a Abstract Harmonic Analysis. $3 891093
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Graduate texts in mathematics ; $v 302. $3 3723307
856 4 0 $u https://doi.org/10.1007/978-3-031-56500-7
950 $a Mathematics and Statistics (SpringerNature-11649)