LEADER 04261nam 22007815 450 001 9910299772403321 005 20200702180220.0 010 $a3-0348-0887-9 024 7 $a10.1007/978-3-0348-0887-3 035 $a(CKB)3710000000343724 035 $a(SSID)ssj0001424410 035 $a(PQKBManifestationID)11748698 035 $a(PQKBTitleCode)TC0001424410 035 $a(PQKBWorkID)11362637 035 $a(PQKB)11060981 035 $a(DE-He213)978-3-0348-0887-3 035 $a(MiAaPQ)EBC6315294 035 $a(MiAaPQ)EBC5586677 035 $a(Au-PeEL)EBL5586677 035 $a(OCoLC)1026450721 035 $a(PPN)183520335 035 $a(EXLCZ)993710000000343724 100 $a20150121d2015 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aAnalysis on h-Harmonics and Dunkl Transforms /$fby Feng Dai, Yuan Xu ; edited by Sergey Tikhonov 205 $a1st ed. 2015. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2015. 215 $a1 online resource (VIII, 118 p.) 225 1 $aAdvanced Courses in Mathematics - CRM Barcelona,$x2297-0304 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-0348-0886-0 327 $aPreface -- 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. 330 $aAs a unique case in this Advanced Courses book series, the authors have jointly written this introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The theory, originally introduced by C. Dunkl, has been expanded on by many authors over the last 20 years. These notes provide an overview of what has been developed so far. The first chapter gives a brief recount of the basics of ordinary spherical harmonics and the Fourier transform. The Dunkl operators, the intertwining operators between partial derivatives and the Dunkl operators are introduced and discussed in the second chapter. The next three chapters are devoted to analysis on the sphere, and the final two chapters to the Dunkl transform. The authors? focus is on the analysis side of both h-harmonics and Dunkl transforms. The need for background knowledge on reflection groups is kept to a bare minimum. 410 0$aAdvanced Courses in Mathematics - CRM Barcelona,$x2297-0304 606 $aApproximation theory 606 $aHarmonic analysis 606 $aIntegral transforms 606 $aOperational calculus 606 $aFunctional analysis 606 $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023 606 $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015 606 $aIntegral Transforms, Operational Calculus$3https://scigraph.springernature.com/ontologies/product-market-codes/M12112 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aApproximation theory. 615 0$aHarmonic analysis. 615 0$aIntegral transforms. 615 0$aOperational calculus. 615 0$aFunctional analysis. 615 14$aApproximations and Expansions. 615 24$aAbstract Harmonic Analysis. 615 24$aIntegral Transforms, Operational Calculus. 615 24$aFunctional Analysis. 676 $a515.2433 676 $a515.2433 700 $aDai$b Feng$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755517 702 $aXu$b Yuan$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTikhonov$b Sergey$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299772403321 996 $aAnalysis on h-Harmonics and Dunkl Transforms$92504062 997 $aUNINA