Heat Kernel Analysis on Lie Groups

2001 ◽  
pp. 1-58 ◽  
Author(s):  
L. Gross
Keyword(s):  
Heat Kernel ◽  
Lie Groups ◽  
Kernel Analysis ◽  
Heat Kernel Analysis

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.

scholarly journals Heat Kernel Analysis of Syntactic Structures

2021 ◽  
Author(s):  
Andrew Ortegaray ◽  
Robert C. Berwick ◽  
Matilde Marcolli
Keyword(s):  
Heat Kernel ◽  
Syntactic Structures ◽  
Kernel Analysis ◽  
Heat Kernel Analysis
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