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Record Nr. |
UNISA996466598403316 |
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Autore |
Schürmann Michael <1955-> |
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Titolo |
White noise on bialgebras / / Michael Schürmann |
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Pubbl/distr/stampa |
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Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1993] |
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©1993 |
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ISBN |
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Edizione |
[1st ed. 1993.] |
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Descrizione fisica |
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1 online resource (VI, 146 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1544 |
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Disciplina |
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Soggetti |
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Quantum theory - Mathematics |
Global analysis (Mathematics) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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Basic 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. |
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Sommario/riassunto |
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Stochastic 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. |
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