Neuenschwander, Daniel.
Probabilities on the Heisenberg Group Limit Theorems and Brownian Motion / [electronic resource] : by Daniel Neuenschwander. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1996. - VIII, 148 p. online resource. - Lecture Notes in Mathematics, 1630 0075-8434 ; . - Lecture Notes in Mathematics, 1630 .
Probability theory on simply connected nilpotent Lie groups -- Brownian motions on H -- Other limit theorems on H.
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.
9783540685906
10.1007/BFb0094029 doi
Mathematics.
Topological Groups.
Distribution (Probability theory).
Mathematical physics.
Mathematics.
Probability Theory and Stochastic Processes.
Topological Groups, Lie Groups.
Mathematical and Computational Physics.
Numerical and Computational Methods in Engineering.
QA273.A1-274.9 QA274-274.9
519.2
Probabilities on the Heisenberg Group Limit Theorems and Brownian Motion / [electronic resource] : by Daniel Neuenschwander. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1996. - VIII, 148 p. online resource. - Lecture Notes in Mathematics, 1630 0075-8434 ; . - Lecture Notes in Mathematics, 1630 .
Probability theory on simply connected nilpotent Lie groups -- Brownian motions on H -- Other limit theorems on H.
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.
9783540685906
10.1007/BFb0094029 doi
Mathematics.
Topological Groups.
Distribution (Probability theory).
Mathematical physics.
Mathematics.
Probability Theory and Stochastic Processes.
Topological Groups, Lie Groups.
Mathematical and Computational Physics.
Numerical and Computational Methods in Engineering.
QA273.A1-274.9 QA274-274.9
519.2