LEADER 02948nam 2200601 450 001 996466598403316 005 20231207002253.0 010 $a3-540-47614-8 024 7 $a10.1007/BFb0089237 035 $a(CKB)1000000000437145 035 $a(SSID)ssj0000327638 035 $a(PQKBManifestationID)12062365 035 $a(PQKBTitleCode)TC0000327638 035 $a(PQKBWorkID)10303705 035 $a(PQKB)10207539 035 $a(DE-He213)978-3-540-47614-6 035 $a(MiAaPQ)EBC5592291 035 $a(Au-PeEL)EBL5592291 035 $a(OCoLC)1066180616 035 $a(MiAaPQ)EBC6841986 035 $a(Au-PeEL)EBL6841986 035 $a(PPN)155219243 035 $a(EXLCZ)991000000000437145 100 $a20220908d1993 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aWhite noise on bialgebras /$fMichael Schu?rmann 205 $a1st ed. 1993. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1993] 210 4$dİ1993 215 $a1 online resource (VI, 146 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1544 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-56627-9 327 $aBasic concepts and first results -- Symmetric white noise on Bose Fock space -- Symmetrization -- White noise on bose fock space -- Quadratic components of conditionally positive linear functionals -- Limit theorems. 330 $aStochastic processes with independent increments on a group are generalized to the concept of "white noise" on a Hopf algebra or bialgebra. The main purpose of the book is the characterization of these processes as solutions of quantum stochastic differential equations in the sense of R.L. Hudson and K.R. Parthasarathy. The notes are a contribution to quantum probability but they are also related to classical probability, quantum groups, and operator algebras. The Az ma martingales appear as examples of white noise on a Hopf algebra which is a deformation of the Heisenberg group. The book will be of interest to probabilists and quantum probabilists. Specialists in algebraic structures who are curious about the role of their concepts in probability theory as well as quantum theory may find the book interesting. The reader should have some knowledge of functional analysis, operator algebras, and probability theory. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1544 606 $aQuantum theory$xMathematics 606 $aGlobal analysis (Mathematics)$vCongresses 615 0$aQuantum theory$xMathematics. 615 0$aGlobal analysis (Mathematics) 676 $a530.12015192 700 $aSchu?rmann$b Michael$f1955-$0441096 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466598403316 996 $aWhite noise on bialgebras$978682 997 $aUNISA