03219nam 22006495 450 99646647330331620200630233647.03-540-31552-710.1007/b104912(CKB)1000000000231910(DE-He213)978-3-540-31552-0(SSID)ssj0000315664(PQKBManifestationID)11211609(PQKBTitleCode)TC0000315664(PQKBWorkID)10264542(PQKB)10831768(MiAaPQ)EBC6283451(MiAaPQ)EBC4976043(Au-PeEL)EBL4976043(CaONFJC)MIL140212(OCoLC)1024261838(PPN)123090938(EXLCZ)99100000000023191020100806d2005 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierAbstract Harmonic Analysis of Continuous Wavelet Transforms[electronic resource] /by Hartmut Führ1st ed. 2005.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2005.1 online resource (X, 193 p.)Lecture Notes in Mathematics,0075-8434 ;1863Bibliographic Level Mode of Issuance: Monograph3-540-24259-7 Includes bibliographical references (pages [185]-190) and index.Introduction -- Wavelet Transforms and Group Representations -- The Plancherel Transform for Locally Compact Groups -- Plancherel Inversion and Wavelet Transforms -- Admissible Vectors for Group Extension -- Sampling Theorems for the Heisenberg Group -- References -- Index.This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a – reasonably self-contained – exposition of Plancherel theory. Therefore, the book can also be read as a problem-driven introduction to the Plancherel formula.Lecture Notes in Mathematics,0075-8434 ;1863Harmonic analysisFourier analysisAbstract Harmonic Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12015Fourier Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12058Harmonic analysis.Fourier analysis.Abstract Harmonic Analysis.Fourier Analysis.515.2433Führ Hartmutauthttp://id.loc.gov/vocabulary/relators/aut472490MiAaPQMiAaPQMiAaPQBOOK996466473303316Abstract harmonic analysis of continuous wavelet transforms230757UNISA