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Probabilistic Trace and Poisson Summation Formulae on Locally Compact Abelian Groups
[article]

2016
*
arXiv
*
pre-print

We investigate convolution

arXiv:1602.01252v4
fatcat:7vk5xf3aurc2djgqych7jryyy4
*semigroups**of*probability measures with continuous densities on locally compact*abelian**groups*, which have a discrete subgroup such that the factor*group*is compact. ... Our main result is to show that the Poisson*summation*formula*for*the density can be interpreted as a probabilistic trace formula, linking values*of*the density on the factor*group*to the trace*of*the ... I am very grateful to Nick Bingham*for*reading a draft*of*the manuscript,*and*providing some very helpful comments. ...##
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Probabilistic trace and Poisson summation formulae on locally compact abelian groups

2017
*
Forum mathematicum
*

AbstractWe investigate convolution

doi:10.1515/forum-2016-0067
fatcat:gbhl6puyt5ftxk7arqfmkhblaa
*semigroups**of*probability measures with continuous densities on locally compact*abelian**groups*, which have a discrete subgroup such that the factor*group*is compact. ... Two interesting examples*of*the quotient structure are the ... I am very grateful to Nick Bingham*for*reading a draft*of*the manuscript,*and*providing some very helpful comments,*and*the referee*for*some valuable observations. ...##
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Probabilistic trace and Poisson summation formulae on locally compact abelian groups

2017
*
Forum mathematicum
*

We investigate convolution

doi:10.1515/forum-2017-0049
fatcat:wce22xhxpfeojlaj2wpxaijoly
*semigroups**of*probability measures with continuous densities on locally compact*abelian**groups*, which have a discrete subgroup such that the factor*group*is compact. ... Our main result is to show that the Poisson*summation*formula*for*the density can be interpreted as a probabilistic trace formula, linking values*of*the density on the factor*group*to the trace*of*the ... I am very grateful to Nick Bingham*for*reading a draft*of*the manuscript,*and*providing some very helpful comments,*and*the referee*for*some valuable observations. ...##
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On the Rédei zeta function

1980
*
Journal of Number Theory
*

LATTICES

doi:10.1016/0022-314x(80)90034-7
fatcat:zujiwp7amredhlh2dwk6nj7sp4
*OF*FINITE*ABELIAN**GROUPS**AND*THE CRITICAL*PROBLEM*A lattice L is said to be a lattice*of*(jinite)*abelian**groups*if the following three conditions hold: (a) the elements*of*L are finite*abelian*... Let w be a finite*abelian**group*; then the lattice L(w)*of*all its subgroups is a lattice*of**abelian**groups*. Now, let w be an arbitrary*abelian**group*,*and*{ai} a collection*of*finite subgroups*of*w. ...##
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Analytic and arithmetic theory of semigroups with divisor theory

1992
*
Séminaire de Théorie des Nombres de Bordeaux
*

Skula

doi:10.5802/jtnb.72
fatcat:yllh2kq4lnezzlivh3z7dgyvwe
*of*subsets H*of*a finite*abelian**group*G with A(H) = 0.*For*this we*define*the cross number ,*of*a block B E 8(G). PROPOSITION 6. ... Let G be a finite*abelian**group**of*order h, h =*and*Xi a non-trivial real character*of*G. ...##
###
The Khinchin-Kahane inequality and Banach space embeddings for metric groups
[article]

2016
*
arXiv
*
pre-print

We also show how to use it to

arXiv:1610.03037v1
fatcat:52kyekonmjgcjj4ivwmmxwwwzm
*define*the expectation*of*random variables with values in arbitrary*abelian*normed metric*semigroups*. ... We also provide an alternate proof*for*normed metric*groups*as a consequence*of*a general "transfer principle". ... We would also like to thank David Montague*and*Doug Sparks*for*carefully going through an early draft*of*the paper*and*providing detailed feedback, which improved the exposition. ...##
###
Wrapping Brownian motion and heat kernels on compact Lie groups
[article]

2006
*
arXiv
*
pre-print

We briefly demonstrate how the results on $R^n$ concerning the heat kernel

arXiv:math/0604500v1
fatcat:rucuj4ku6bffdhd4jwafxbdpme
*and*Brownian motion may be easily transferred to compact Lie*groups*using the wrapping map*of*Dooley*and*Wildberger. ... Similar statements hold when $\R^n$ is replaced by a Lie*group*. ... • We would also like to know the L p − L q bounds*for*a wrapped function.*For*example,*for*what p*and*q do we have Φ(u) p ≤ u q ? ...##
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An algebraic approach to discrete dilations. Application to discrete wavelet transforms

2000
*
Journal of Fourier Analysis and Applications
*

The discrete approach is formulated abstractly in terms

doi:10.1007/bf02510656
fatcat:zdhsyf5nqbhtvgisifl5mxor4u
*of*the action*of*a semidirect product A × Γ on ℓ 2 (Γ), with Γ a lattice*and*A an*abelian**semigroup*acting on Γ. ... We investigate the connections between continuous*and*discrete wavelet transforms on the basis*of*algebraic arguments. ... ,*and*the Laboratoire d'Analyse, Topologie et Probabilités, Université de Provence, Marseille. ...##
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Central limit theorem for commutative semigroups of toral endomorphisms
[article]

2013
*
arXiv
*
pre-print

A CLT is also proved

arXiv:1304.4556v2
fatcat:px6ikjd3fjbb5j3wubm7rjcmjy
*for*some*semigroups**of*endomorphisms. Classical results on the existence*and*the construction*of*such actions by automorphisms are recalled. ... Let $\Cal S$ be an*abelian*finitely generated*semigroup**of*endomorphisms*of*a probability space $(\Omega, {\Cal A}, \mu)$, with $(T_1, ..., T_d)$ a system*of*generators in ${\Cal S}$. ... Acknowlegements This research was carried out during visits*of*the first author to the University*of*Rennes 1*and**of*the second author to the Center*for*Advanced Studies in Mathematics at Ben Gurion University ...##
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Revisiting Algebra and Complexity of Inference in Graphical Models
[article]

2015
*
arXiv
*
pre-print

propagation can leverage this distributive law to perform polynomial-time inference

arXiv:1409.7410v4
fatcat:s2jnwiaxvrawrehtpou6cot2fi
*for*certain*problems*. ... In particular, we broadly formalize inference*problems*in graphical models by viewing them as a sequence*of*operations based on commutative*semigroups*. ... -The set*of*natural numbers N with*summation**defines*a commutative*semigroup*. -Integers modulo n with addition*defines*an*Abelian**group*. ...##
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Minimal systems of generators for ideals of semigroups

1998
*
Journal of Pure and Applied Algebra
*

We give an algorithmic method to compute a minimal system

doi:10.1016/s0022-4049(96)00106-5
fatcat:4pu2gx7ponbmpecpfvylommyvi
*of*generators*for*I, in the general case*of*a subsemigroup Sofa finitely generated*abelian**group*, such that Sc~(-S) = {0}. ... We shall denote by G(S) the associated*abelian**group*, i.e., Let G be an*abelian**group**and*let j: S --* G be a*semigroup*homomorphism. ... Now, we will describe the solutions to both*problems*in case one has a concrete embedding*of*S into a finitely generated*abelian**group*G = F • T, where F is a free*abelian**group**and*T a torsion*group*. ...##
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The Brown Mccoy radical of semigroup rings of commutative cancellative semigroups

1985
*
Glasgow Mathematical Journal
*

Let R

doi:10.1017/s0017089500005863
fatcat:o7h7odogorcfbml2lrpxmu3kza
*and*T be rings such that T is a normalizing extension*of*R. Then Proof, cf. [9] or [11]. PROPOSITION 1.2. (1) Let G be a finite*abelian**group**of*order n*and*let R be a G-graded ring. ... Note that the condition that R*and*S have a unity can be dropped (cf. [8]). The quotient*group**of*S is denoted by Q(S). ... Before proving the main theorem we need a lemma about the Brown-McCoy radical*of*a*group*ring*of*a finite*abelian**group*. ...##
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Small doubling in ordered semigroups

2014
*
Semigroup Forum
*

In particular, we show by Proposition 6 that every

doi:10.1007/s00233-014-9603-2
fatcat:pwt6726dk5aidgxqzmca7trrle
*abelian*torsion-free cancellative*semigroup*is linearly orderable, so extending a similar 1913 result*of*F.W. Levi on*abelian*torsion-free*groups*. ... Herzog*and*coauthors on the structure theory*of*product-sets from the context*of*linearly (i.e., strictly*and*totally) ordered*groups*to linearly ordered*semigroups*. ...*For*what it is worth, note that the*summation*in (7) involves only a finite number*of*non-zero terms*for*every φ, which makes the Cauchy product well-*defined*even if X is infinite. ...##
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On finite invariant measures for Markov operators

1973
*
Proceedings of the American Mathematical Society
*

Two lemmas on proper vectors

doi:10.1090/s0002-9939-1973-0312318-5
fatcat:6uqn7wzf4jftflmbyndmqdac54
*of*convex linear combination*of*operators*and**semigroups*in a Banach space are proved. They are applied to*problems**of*invariant measures*for*Markov operators. ... Lemma 2 (*and*Theorem 2) hold*for*the general case*of*a strongly continuous operator representation by operators*of*norm 1,*of*a locally compact connected*and*metrizable*Abelian**group*. ... To see that, consider ñm\\E\ i Let us consider a strongly continuous*semigroup**of*operators on £, £,, with ||£(||_1. ...##
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On Finite Invariant Measures for Markov Operators

1973
*
Proceedings of the American Mathematical Society
*

Two lemmas on proper vectors

doi:10.2307/2038949
fatcat:22lze5n7ajhvfjniynpligqg6m
*of*convex linear combination*of*operators*and**semigroups*in a Banach space are proved. They are applied to*problems**of*invariant measures*for*Markov operators. ... Lemma 2 (*and*Theorem 2) hold*for*the general case*of*a strongly continuous operator representation by operators*of*norm 1,*of*a locally compact connected*and*metrizable*Abelian**group*. ... To see that, consider ñm\\E\ i Let us consider a strongly continuous*semigroup**of*operators on £, £,, with ||£(||_1. ...
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