國立虎尾科技大學 |

Analysis on h-Harmonics and Dunkl Transforms

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Analysis on h-Harmonics and Dunkl Transforms/ by Feng Dai, Yuan Xu ; edited by Sergey Tikhonov.
Author:	Dai, Feng.
other author:	Xu, Yuan.
Description:	VIII, 118 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Approximation theory. -
Online resource:	https://doi.org/10.1007/978-3-0348-0887-3
ISBN:	9783034808873

Analysis on h-Harmonics and Dunkl Transforms
Dai, Feng.

Analysis on h-Harmonics and Dunkl Transforms[electronic resource] /by Feng Dai, Yuan Xu ; edited by Sergey Tikhonov. - 1st ed. 2015. - VIII, 118 p.online resource. - Advanced Courses in Mathematics - CRM Barcelona,2297-0304. - Advanced Courses in Mathematics - CRM Barcelona,.

Preface -- Spherical harmonics and Fourier transform -- Dunkl operators associated with reflection groups -- h-Harmonics and analysis on the sphere -- Littlewood–Paley theory and the multiplier theorem -- Sharp Jackson and sharp Marchaud inequalities -- Dunkl transform -- Multiplier theorems for the Dunkl transform -- Bibliography.

As a unique case in this Advanced Courses book series, the authors have jointly written this introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The theory, originally introduced by C. Dunkl, has been expanded on by many authors over the last 20 years. These notes provide an overview of what has been developed so far. The first chapter gives a brief recount of the basics of ordinary spherical harmonics and the Fourier transform. The Dunkl operators, the intertwining operators between partial derivatives and the Dunkl operators are introduced and discussed in the second chapter. The next three chapters are devoted to analysis on the sphere, and the final two chapters to the Dunkl transform. The authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms. The need for background knowledge on reflection groups is kept to a bare minimum.

ISBN: 9783034808873

Standard No.: 10.1007/978-3-0348-0887-3doiSubjects--Topical Terms:

527707
Approximation theory.

LC Class. No.: QA401-425

Dewey Class. No.: 511.4

Analysis on h-Harmonics and Dunkl Transforms
LDR:02741nam a22003975i 4500 001 962392
003 DE-He213
005 20200702180220.0
007 cr nn 008mamaa
008 201211s2015 sz | s |||| 0|eng d
020 $a 9783034808873 $9 978-3-0348-0887-3
024 7 $a 10.1007/978-3-0348-0887-3 $2 doi
035 $a 978-3-0348-0887-3
050 4 $a QA401-425
072 7 $a PBKJ $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 511.4 $2 23
100 1 $a Dai, Feng. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1065976
245 1 0 $a Analysis on h-Harmonics and Dunkl Transforms $h [electronic resource] / $c by Feng Dai, Yuan Xu ; edited by Sergey Tikhonov.
250 $a 1st ed. 2015.
264 1 $a Basel : $b Springer Basel : $b Imprint: Birkhäuser, $c 2015.
300 $a VIII, 118 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Advanced Courses in Mathematics - CRM Barcelona, $x 2297-0304
505 0 $a Preface -- Spherical harmonics and Fourier transform -- Dunkl operators associated with reflection groups -- h-Harmonics and analysis on the sphere -- Littlewood–Paley theory and the multiplier theorem -- Sharp Jackson and sharp Marchaud inequalities -- Dunkl transform -- Multiplier theorems for the Dunkl transform -- Bibliography.
520 $a As a unique case in this Advanced Courses book series, the authors have jointly written this introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The theory, originally introduced by C. Dunkl, has been expanded on by many authors over the last 20 years. These notes provide an overview of what has been developed so far. The first chapter gives a brief recount of the basics of ordinary spherical harmonics and the Fourier transform. The Dunkl operators, the intertwining operators between partial derivatives and the Dunkl operators are introduced and discussed in the second chapter. The next three chapters are devoted to analysis on the sphere, and the final two chapters to the Dunkl transform. The authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms. The need for background knowledge on reflection groups is kept to a bare minimum.
650 0 $a Approximation theory. $3 527707
650 0 $a Harmonic analysis. $3 672073
650 0 $a Integral transforms. $3 678414
650 0 $a Operational calculus. $3 1253881
650 0 $a Functional analysis. $3 527706
650 1 4 $a Approximations and Expansions. $3 672153
650 2 4 $a Abstract Harmonic Analysis. $3 672075
650 2 4 $a Integral Transforms, Operational Calculus. $3 672154
650 2 4 $a Functional Analysis. $3 672166
700 1 $a Xu, Yuan. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1065977
700 1 $a Tikhonov, Sergey. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 1065978
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783034808880
776 0 8 $i Printed edition: $z 9783034808866
830 0 $a Advanced Courses in Mathematics - CRM Barcelona, $x 2297-0304 $3 1257135
856 4 0 $u https://doi.org/10.1007/978-3-0348-0887-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)