Bochner-Riesz means on Euclidean spaces / Shanzhen Lu, Beijing Normal University, China, Dunyan Yan, University of Chinese Academy of Sciences, China.

Format:

Book

Author/Creator:

Lu, Shanzhen, 1939-

Yan, Dunyan, author.

Series:

Gale eBooks

Language:

English

Subjects (All):

Fourier series.

Euclidean algorithm.

Fourier series--Mathematical models.

Euclidean algorithm--Mathematical models.

Physical Description:

1 online resource (viii, 376 pages) : illustrations

Place of Publication:

New Jersey : World Scientific, [2013]

Language Note:

English

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

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed September 16, 2013).

ISBN:

9789814458771

9814458775

OCLC:

860388264