Harmonic analysis on some generalized Gelfand pairs attached to Heisenberg groups

2018 ◽  
Vol 241 (2) ◽  
pp. 135-158
Author(s):  
Fernando Levstein ◽  
Linda Saal
Keyword(s):  
Harmonic Analysis ◽  
Heisenberg Groups ◽  
Gelfand Pairs

scholarly journals Harmonic analysis on the quotient spaces of Heisenberg groups

1991 ◽  
Vol 123 ◽  
pp. 103-117 ◽  
Author(s):  
Jae-Hyun Yang
Keyword(s):  
Quantum Mechanics ◽  
Heisenberg Group ◽  
Harmonic Analysis ◽  
Unitary Representation ◽  
Lie Group ◽  
Theta Series ◽  
Foundations Of Quantum Mechanics ◽  
Nilpotent Lie Group ◽  
Heisenberg Groups ◽  
Quotient Spaces

A certain nilpotent Lie group plays an important role in the study of the foundations of quantum mechanics ([Wey]) and of the theory of theta series (see [C], [I] and [Wei]). This work shows how theta series are applied to decompose the natural unitary representation of a Heisenberg group.

scholarly journals Some results on harmonic analysis on compact quotients of heisenberg groups

1985 ◽  
Vol 99 ◽  
pp. 45-62 ◽  
Author(s):  
Hisasi Morikawa
Keyword(s):  
Heisenberg Group ◽  
Nilpotent Group ◽  
Harmonic Analysis ◽  
Matrix Group ◽  
Heisenberg Groups ◽  
Dimension 2 ◽  
The Law

Heisenberg group H2g+1(R) of dimension 2g + 1 is a real nilpotent group defined on R × Rg × Rg by the law of composition which is isomorphic to the unipotent matrix group

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