Chromatic Expansions and the Bargmann Transform

2012 ◽  
pp. 139-159
Author(s):  
Ahmed I. Zayed
Keyword(s):  
Bargmann Transform

scholarly journals Segal–Bargmann transform and Paley–Wiener theorems on Heisenberg motion groups

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Suparna Sen
Keyword(s):  
Bargmann Transform ◽  
Motion Groups

AbstractWe consider the Heisenberg motion groups ℍ𝕄 = ℍ

A New Form of the Segal-Bargmann Transform for Lie Groups of Compact Type

1999 ◽  
Vol 51 (4) ◽  
pp. 816-834 ◽  
Author(s):  
Brian C. Hall
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Joint Work ◽  
Compact Type ◽  
Bargmann Transform ◽  
Infinite Dimensional ◽  
Infinite Dimensional Analysis ◽  
Finite Dimensional ◽  
New Form ◽  
Two Parameter

AbstractI consider a two-parameter family Bs,t of unitary transforms mapping an L2-space over a Lie group of compact type onto a holomorphic L2-space over the complexified group. These were studied using infinite-dimensional analysis in joint work with B. Driver, but are treated here by finite-dimensional means. These transforms interpolate between two previously known transforms, and all should be thought of as generalizations of the classical Segal-Bargmann transform. I consider also the limiting cases s → ∞ and s → t/2.

Entropy and the Segal-Bargmann transform

1998 ◽  
Vol 39 (4) ◽  
pp. 2402-2417 ◽  
Author(s):  
Stephen Bruce Sontz
Keyword(s):  
Bargmann Transform

The Heisenberg–Weyl group in the coherent state basis and the Bargmann transform

1988 ◽  
Vol 29 (8) ◽  
pp. 1854-1859 ◽  
Author(s):  
Debabrata Basu ◽  
T. K. Kar
Keyword(s):  
Coherent State ◽  
Weyl Group ◽  
Bargmann Transform

scholarly journals The Segal–Bargmann Transform for Odd-Dimensional Hyperbolic Spaces

Mathematics ◽  
2015 ◽  
Vol 3 (3) ◽  
pp. 758-780
Author(s):  
Brian Hall ◽  
Jeffrey Mitchell
Keyword(s):  
Hyperbolic Spaces ◽  
Bargmann Transform

Probabilistic aspects of the SU(2)-harmonic oscillator

2000 ◽  
Vol 37 (1) ◽  
pp. 306-314
Author(s):  
Shunlong Luo
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Probability Distributions ◽  
Quantum Probability ◽  
Dimensional Sphere ◽  
Large Radius ◽  
Two Dimensional ◽  
Bargmann Transform ◽  
Gaussian Distributions ◽  
Binomial Distributions

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

THE μ-DEFORMED SEGAL–BARGMANN TRANSFORM IS A HALL TYPE TRANSFORM

2009 ◽  
Vol 12 (02) ◽  
pp. 269-289 ◽  
Author(s):  
STEPHEN BRUCE SONTZ
Keyword(s):  
Analytic Continuation ◽  
Heat Kernel ◽  
Bargmann Transform ◽  
Kernel Analysis ◽  
Bargmann Transforms ◽  
Heat Kernel Analysis

We present an explanation of how the μ-deformed Segal–Bargmann spaces, that are studied in various articles of the author in collaboration with Angulo, Echavarría and Pita, can be viewed as deserving their name, that is, how they should be considered as a part of Segal–Bargmann analysis. This explanation relates the μ-deformed Segal–Bargmann transforms to the generalized Segal–Bargmann transforms introduced by B. Hall using heat kernel analysis. All the versions of the μ-deformed Segal–Bargmann transform can be understood as Hall type transforms. In particular, we define a μ-deformation of Hall's "Version C" generalized Segal–Bargmann transform which is then shown to be a μ-deformed convolution with a μ-deformed heat kernel followed by analytic continuation. Our results are generalizations and analogues of the results of Hall.

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