02999nam 2200589 450 991048366480332120220511142533.03-540-77911-610.1007/978-3-540-77911-7(CKB)1000000000546225(SSID)ssj0000316196(PQKBManifestationID)11275341(PQKBTitleCode)TC0000316196(PQKBWorkID)10274784(PQKB)10987921(DE-He213)978-3-540-77911-7(MiAaPQ)EBC3063684(MiAaPQ)EBC6708698(Au-PeEL)EBL6708698(PPN)130185183(EXLCZ)99100000000054622520220511d2008 uy 0engurnn|008mamaatxtccrAlternative pseudodifferential analysis with an application to modular forms /André Unterberger1st ed. 2008.Berlin, Germany :Springer,[2008]©20081 online resource (IX, 118 p.) Lecture Notes in Mathematics,0075-8434 ;1935Bibliographic Level Mode of Issuance: Monograph3-540-77910-8 Includes bibliographical references and index.Preface -- Introduction -- The Metaplectic and Anaplectic Representations -- The One-dimensional Alternative Pseudodifferential Analysis -- From Anaplectic Analysis to Usual Analysis -- Pseudodifferential Analysis and Modular Forms -- Index -- Bibliography.This volume introduces an entirely new pseudodifferential analysis on the line, the opposition of which to the usual (Weyl-type) analysis can be said to reflect that, in representation theory, between the representations from the discrete and from the (full, non-unitary) series, or that between modular forms of the holomorphic and substitute for the usual Moyal-type brackets. This pseudodifferential analysis relies on the one-dimensional case of the recently introduced anaplectic representation and analysis, a competitor of the metaplectic representation and usual analysis. Besides researchers and graduate students interested in pseudodifferential analysis and in modular forms, the book may also appeal to analysts and physicists, for its concepts making possible the transformation of creation-annihilation operators into automorphisms, simultaneously changing the usual scalar product into an indefinite but still non-degenerate one.Lecture Notes in Mathematics,0075-8434 ;1935Pseudodifferential operatorsForms, ModularPseudodifferential operators.Forms, Modular.515.7242Unterberger André351381MiAaPQMiAaPQMiAaPQBOOK9910483664803321Alternative pseudodifferential analysis258932UNINA