The Adamjan-Arov-Krein Theorem in General and Regular Representations of R2 and the Symplectic Plane

1994 ◽  
pp. 54-78
Author(s):  
Mischa Cotlar ◽  
Cora Sadosky
Keyword(s):  
Regular Representations ◽  
Krein Theorem

scholarly journals Quantum Heisenberg group and algebra: Contraction, left and right regular representations

1995 ◽  
Vol 36 (3) ◽  
pp. 1404-1412 ◽  
Author(s):  
Demosthenes Ellinas ◽  
Jan Sobczyk
Keyword(s):  
Heisenberg Group ◽  
Regular Representations ◽  
Left And Right ◽  
And Algebra

scholarly journals Unitarization of the Horocyclic Radon Transform on Homogeneous Trees

2021 ◽  
Vol 27 (5) ◽  
Author(s):  
Francesca Bartolucci ◽  
Filippo De Mari ◽  
Matteo Monti
Keyword(s):  
Radon Transform ◽  
Homogeneous Tree ◽  
Homogeneous Trees ◽  
Regular Representations ◽  
Group Of Isometries

AbstractFollowing previous work in the continuous setup, we construct the unitarization of the horocyclic Radon transform on a homogeneous tree X and we show that it intertwines the quasi regular representations of the group of isometries of X on the tree itself and on the space of horocycles.

scholarly journals The Plancherel formula for the horocycle space and generalizations

1996 ◽  
Vol 61 (1) ◽  
pp. 42-56 ◽  
Author(s):  
Ronald L. Lipsman
Keyword(s):  
Harmonic Analysis ◽  
Regular Representation ◽  
Plancherel Formula ◽  
Intertwining Operators ◽  
Direct Integral ◽  
Regular Representations ◽  
Spectral Distributions ◽  
Theoretic Technique ◽  
Direct Integral Decomposition ◽  
Integral Decomposition

AbstractThe Plancherel formula for the horocycle space, and several generalizations, is derived within the framework of quasi-regular representations which have monomial spectrum. The proof uses only machinery from the Penney-Fujiwara distribution-theoretic technique; no special semisimple harmonic analysis is needed. The Plancherel formulas obtained include the spectral distributions and the intertwining operators that effect the direct integral decomposition of the quasi-regular representation.

Graphical Regular Representations of Non-Abelian Groups, II

1972 ◽  
Vol 24 (6) ◽  
pp. 1009-1018 ◽  
Author(s):  
Lewis A. Nowitz ◽  
Mark E. Watkins
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Regular Representation ◽  
Affirmative Answer ◽  
Roman Numeral ◽  
Regular Representations ◽  
Graphical Regular Representation ◽  
Bold Face

The present paper is a sequel to the previous paper bearing the same title by the same authors [3] and which will be hereafter designated by the bold-face Roman numeral I. Further results are obtained in determining whether a given finite non-abelian group G has a graphical regular representation. In particular, an affirmative answer will be given if (|G|, 6) = 1.Inasmuch as much of the machinery of I will be required in the proofs to be presented and a perusal of I is strongly recommended to set the stage and provide motivation for this paper, an independent and redundant introduction will be omitted in the interest of economy.

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