On the theorem on asymptotic equidistribution of the convolution powers of symmetric measures on a unimodular group

1996 ◽  
Vol 60 (1) ◽  
pp. 89-93 ◽  
Author(s):  
M. G. Shur
Keyword(s):  
Unimodular Group ◽  
Convolution Powers ◽  
Asymptotic Equidistribution

scholarly journals On the classification of isotropic tensors

1987 ◽  
Vol 29 (2) ◽  
pp. 185-196 ◽  
Author(s):  
P. G. Appleby ◽  
B. R. Duffy ◽  
R. W. Ogden
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Final Section ◽  
Complete Classification ◽  
Coordinate Transformations ◽  
Tensor Fields ◽  
Isotropic Tensor ◽  
Unimodular Group ◽  
Derivatives Of

A tensor is said to be isotropic relative to a group of transformations if its components are invariant under the associated group of coordinate transformations. In this paper we review the classification of tensors which are isotropic under the general linear group, the special linear (unimodular) group and the rotational group. These correspond respectively to isotropic absolute tensors [4, 8] isotropic relative tensors [4] and isotropic Cartesian tensors [3]. New proofs are given for the representation of isotropic tensors in terms of Kronecker deltas and alternating tensors. And, for isotropic Cartesian tensors, we provide a complete classification, clarifying results described in [3].In the final section of the paper certain derivatives of isotropic tensor fields are examined.

scholarly journals DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS

2014 ◽  
Vol 57 (3) ◽  
pp. 693-707
Author(s):  
YEMON CHOI
Keyword(s):  
Invertible Element ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Complex Line ◽  
Locally Compact ◽  
The Real ◽  
C Algebra ◽  
Finite Algebras ◽  
Unimodular Group ◽  
Reduced Group

AbstractAn algebraAis said to be directly finite if each left-invertible element in the (conditional) unitization ofAis right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras ofp-pseudofunctions, showing that these algebras are directly finite ifGis amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply thatL1(G) is not directly finite whenGis the affine group of either the real or complex line.

scholarly journals Two-element generation of the projective unimodular group

1959 ◽  
Vol 3 (3) ◽  
pp. 421-439 ◽  
Author(s):  
A. A. Albert ◽  
John Thompson
Keyword(s):  
Unimodular Group

scholarly journals Automorphisms of the Gaussian unimodular group

1958 ◽  
Vol 87 (1) ◽  
pp. 76-76 ◽  
Author(s):  
Joseph Landin ◽  
Irving Reiner
Keyword(s):  
Unimodular Group

Analysis of the Luria–Delbrück distribution using discrete convolution powers

1992 ◽  
Vol 29 (02) ◽  
pp. 255-267 ◽  
Author(s):  
W. T. Ma ◽  
G. vH. Sandri ◽  
S. Sarkar
Keyword(s):  
Population Genetics ◽  
Asymptotic Behavior ◽  
Computational Efficiency ◽  
Recursion Relation ◽  
Expected Number ◽  
Discrete Convolution ◽  
Convolution Powers ◽  
Central Result

The Luria–Delbrück distribution arises in birth-and-mutation processes in population genetics that have been systematically studied for the last fifty years. The central result reported in this paper is a new recursion relation for computing this distribution which supersedes all past results in simplicity and computational efficiency: p 0 = e–m ; where m is the expected number of mutations. A new relation for the asymptotic behavior of pn (≈ c/n 2) is also derived. This corresponds to the probability of finding a very large number of mutants. A formula for the z-transform of the distribution is also reported.

scholarly journals Convolution powers of complex functions on $\mathbb Z^d$

2017 ◽  
Vol 33 (3) ◽  
pp. 1045-1121 ◽  
Author(s):  
Evan Randles ◽  
Laurent Saloff-Coste
Keyword(s):  
Complex Functions ◽  
Convolution Powers
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