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Probabilities on the Heisenberg group : limit theorems and Brownian motion / Daniel Neuenschwander.

By: Neuenschwander, Daniel, 1963-Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1630.Publication details: Berlin ; New York : Springer, ©1996. Description: 1 online resource (viii, 139 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540685906; 3540685901Subject(s): Nilpotent Lie groups | Probability measures | Limit theorems (Probability theory) | Brownian motion processes | Groupes de Lie nilpotents | Mesures de probabilités | Théorèmes limites (Théorie des probabilités) | Processus de mouvement brownien | Brownian motion processes | Limit theorems (Probability theory) | Nilpotent Lie groups | Probability measures | Limiettheorema's | Distribuicoes (probabilidade) | Processos markovianosGenre/Form: Electronic books. Additional physical formats: Print version:: Probabilities on the Heisenberg group.DDC classification: 510 s | 519.2/6 LOC classification: QA3 | .L28 no. 1630 | QA387Other classification: 31.70 Online resources: Click here to access online
Contents:
1. Probability theory on simply connected nilpotent Lie groups -- 2. Brownian motions on [actual symbol not reproducible] -- 3. Other limit theorems on [actual symbol not reproducible].
Summary: The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.
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Includes bibliographical references (pages 125-136) and index.

The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.

1. Probability theory on simply connected nilpotent Lie groups -- 2. Brownian motions on [actual symbol not reproducible] -- 3. Other limit theorems on [actual symbol not reproducible].

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