Filters








1,023 Hits in 5.2 sec

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

David Applebaum
2016 arXiv   pre-print
We investigate convolution 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.  ... 
arXiv:1602.01252v4 fatcat:7vk5xf3aurc2djgqych7jryyy4

Probabilistic trace and Poisson summation formulae on locally compact abelian groups

David Applebaum
2017 Forum mathematicum  
AbstractWe investigate convolution 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.  ... 
doi:10.1515/forum-2016-0067 fatcat:gbhl6puyt5ftxk7arqfmkhblaa

Probabilistic trace and Poisson summation formulae on locally compact abelian groups

David Applebaum
2017 Forum mathematicum  
We investigate convolution 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.  ... 
doi:10.1515/forum-2017-0049 fatcat:wce22xhxpfeojlaj2wpxaijoly

On the Rédei zeta function

Joseph P.S. Kung, M.Ram Murty, Gian-Carlo Rota
1980 Journal of Number Theory  
LATTICES 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.  ... 
doi:10.1016/0022-314x(80)90034-7 fatcat:zujiwp7amredhlh2dwk6nj7sp4

Analytic and arithmetic theory of semigroups with divisor theory

Alfred Geroldinger, Jerzy Kaczorowski
1992 Séminaire de Théorie des Nombres de Bordeaux  
Skula 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.  ... 
doi:10.5802/jtnb.72 fatcat:yllh2kq4lnezzlivh3z7dgyvwe

The Khinchin-Kahane inequality and Banach space embeddings for metric groups [article]

Apoorva Khare, Bala Rajaratnam
2016 arXiv   pre-print
We also show how to use it to 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.  ... 
arXiv:1610.03037v1 fatcat:52kyekonmjgcjj4ivwmmxwwwzm

Wrapping Brownian motion and heat kernels on compact Lie groups [article]

David Maher
2006 arXiv   pre-print
We briefly demonstrate how the results on $R^n$ concerning the heat kernel 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 ?  ... 
arXiv:math/0604500v1 fatcat:rucuj4ku6bffdhd4jwafxbdpme

An algebraic approach to discrete dilations. Application to discrete wavelet transforms

J. -P. Antoine, Y. B. Kouagou, D. Lambert, B. Torrésani
2000 Journal of Fourier Analysis and Applications  
The discrete approach is formulated abstractly in terms 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.  ... 
doi:10.1007/bf02510656 fatcat:zdhsyf5nqbhtvgisifl5mxor4u

Central limit theorem for commutative semigroups of toral endomorphisms [article]

Guy Cohen, Jean-Pierre Conze
2013 arXiv   pre-print
A CLT is also proved 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  ... 
arXiv:1304.4556v2 fatcat:px6ikjd3fjbb5j3wubm7rjcmjy

Revisiting Algebra and Complexity of Inference in Graphical Models [article]

Siamak Ravanbakhsh, Russell Greiner
2015 arXiv   pre-print
propagation can leverage this distributive law to perform polynomial-time inference 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.  ... 
arXiv:1409.7410v4 fatcat:s2jnwiaxvrawrehtpou6cot2fi

Minimal systems of generators for ideals of semigroups

E. Briales, A. Campillo, C. Marijuán, P. Pisón
1998 Journal of Pure and Applied Algebra  
We give an algorithmic method to compute a minimal system 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.  ... 
doi:10.1016/s0022-4049(96)00106-5 fatcat:4pu2gx7ponbmpecpfvylommyvi

The Brown Mccoy radical of semigroup rings of commutative cancellative semigroups

E. Jespers, J. Krempa, P. Wauters
1985 Glasgow Mathematical Journal  
Let R 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.  ... 
doi:10.1017/s0017089500005863 fatcat:o7h7odogorcfbml2lrpxmu3kza

Small doubling in ordered semigroups

Salvatore Tringali
2014 Semigroup Forum  
In particular, we show by Proposition 6 that every 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.  ... 
doi:10.1007/s00233-014-9603-2 fatcat:pwt6726dk5aidgxqzmca7trrle

On finite invariant measures for Markov operators

M. Falkowitz
1973 Proceedings of the American Mathematical Society  
Two lemmas on proper vectors 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.  ... 
doi:10.1090/s0002-9939-1973-0312318-5 fatcat:6uqn7wzf4jftflmbyndmqdac54

On Finite Invariant Measures for Markov Operators

M. Falkowitz
1973 Proceedings of the American Mathematical Society  
Two lemmas on proper vectors 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.  ... 
doi:10.2307/2038949 fatcat:22lze5n7ajhvfjniynpligqg6m
« Previous Showing results 1 — 15 out of 1,023 results