Harmonic analysis on homogeneous manifolds of reductive type and unitary representation theory

1997 ◽  
pp. 1-31 ◽  
Author(s):  
Toshiyuki Kobayashi
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Unitary Representation ◽  
Homogeneous Manifolds

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

2009 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Finite Groups ◽  
Wreath Products

scholarly journals Functional Equations and Fourier Analysis

2013 ◽  
Vol 56 (1) ◽  
pp. 218-224 ◽  
Author(s):  
Dilian Yang
Keyword(s):  
Representation Theory ◽  
Fourier Analysis ◽  
Harmonic Analysis ◽  
Functional Equations ◽  
Compact Groups ◽  
Wilson Equation ◽  
D’Alembert Equation

AbstractBy exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation-on compact groups.

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 Studying in Lee groups and most important examples of it (Heisenberg group): دراسة في زمر لي وأهم الأمثلة عنها (زمرة هايزنبرغ)

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Soha Ali Salamah
Keyword(s):  
Number Theory ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Representation Theory ◽  
Heisenberg Group ◽  
Harmonic Analysis ◽  
Lie Groups ◽  
General Definition ◽  
Nilpotent Lie Groups ◽  
Basic Facts

In this research, we present some basic facts about Lie algebra and Lie groups. We shall require only elementary facts about the general definition and knowledge of a few of the more basic groups, such as Euclidean groups. Then we introduce the Heisenberg group which is the most well-known example from the realm of nilpotent Lie groups and plays an important role in several branches of mathematics, such as representation theory, partial differential equations and number theory... It also offers the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis.

Representation Theory and Harmonic Analysis

2010 ◽  
pp. 3043-3083
Author(s):  
Toshiyuki Kobayashi ◽  
Bernhard Krötz
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis

THE CLASSICAL LIMIT OF REPRESENTATION THEORY OF THE QUANTUM PLANE

2013 ◽  
Vol 24 (04) ◽  
pp. 1350031 ◽  
Author(s):  
IVAN C. H. IP
Keyword(s):  
Fourier Transform ◽  
Representation Theory ◽  
Unitary Representation ◽  
Classical Limit ◽  
Mellin Transform ◽  
Tensor Products ◽  
Quantum Plane ◽  
The Fourier Transform

We showed that there is a complete analogue of a representation of the quantum plane [Formula: see text] where |q| = 1, with the classical ax+b group. We showed that the Fourier transform of the representation of [Formula: see text] on [Formula: see text] has a limit (in the dual corepresentation) toward the Mellin transform of the unitary representation of the ax+b group, and furthermore the intertwiners of the tensor products representation has a limit toward the intertwiners of the Mellin transform of the classical ax+b representation. We also wrote explicitly the multiplicative unitary defining the quantum ax+b semigroup and showed that it defines the corepresentation that is dual to the representation of [Formula: see text] above, and also correspond precisely to the classical family of unitary representation of the ax+b group.

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