共查询到20条相似文献,搜索用时 15 毫秒
1.
G.M. Feldman 《Journal of Functional Analysis》2010,258(12):3977-3987
We prove a group analogue of the well-known Heyde theorem where a Gaussian measure is characterized by the symmetry of the conditional distribution of one linear form given another. Let X be a locally compact second countable Abelian group containing no subgroup topologically isomorphic to the circle group T, G be the subgroup of X generated by all elements of order 2, and Aut(X) be the set of all topological automorphisms of X. Let αj,βj∈Aut(X), j=1,2,…,n, n?2, such that for all i≠j. Let ξj be independent random variables with values in X and distributions μj with non-vanishing characteristic functions. If the conditional distribution of L2=β1ξ1+?+βnξn given L1=α1ξ1+?+αnξn is symmetric, then each μj=γj∗ρj, where γj are Gaussian measures, and ρj are distributions supported in G. 相似文献
2.
Osamu Hatori 《Proceedings of the American Mathematical Society》1998,126(8):2351-2353
Every bounded regular Borel measure on noncompact LCA groups is a sum of an absolutely continuous measure and a measure with natural spectrum. The set of bounded regular Borel measures with natural spectrum on a nondiscrete LCA group whose Fourier-Stieltjes transforms vanish at infinity is closed under addition if and only if is compact.
3.
Vlasta Matijevi? 《Topology and its Applications》2010,157(17):2746-2756
We consider finite-sheeted covering maps from 2-dimensional compact connected abelian groups to Klein bottle weak solenoidal spaces, metric continua which are not groups. We show that whenever a group covers a Klein bottle weak solenoidal space it covers groups as well, moreover it covers the product of two solenoids. The converse is not true, we give an example of group which covers groups with any finite number of sheets, but does not cover any Klein bottle weak solenoidal space. 相似文献
4.
Michael J. Mossinghoff. 《Mathematics of Computation》1998,67(224):1697-1705
We describe several searches for polynomials with integer coefficients and small Mahler measure. We describe the algorithm used to test Mahler measures. We determine all polynomials with degree at most 24 and Mahler measure less than , test all reciprocal and antireciprocal polynomials with height 1 and degree at most 40, and check certain sparse polynomials with height 1 and degree as large as 181. We find a new limit point of Mahler measures near , four new Salem numbers less than , and many new polynomials with small Mahler measure. None has measure smaller than that of Lehmer's degree 10 polynomial.
5.
We prove limit theorems for row sums of a rowwise independent infinitesimal array of random variables with values in a locally compact Abelian group. First we give a proof of Gaiser's theorem [4, Satz 1.3.6], since it does not have an easy access and it is not complete. This theorem gives sufficient conditions for convergence of the row sums, but the limit measure cannot have a nondegenerate idempotent factor. Then we prove necessary and sufficient conditions for convergence of the row sums, where the limit measure can be also a nondegenerate Haar measure on a compact subgroup. Finally, we investigate special cases: the torus group, the group of p ‐adic integers and the p ‐adic solenoid. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
《Mathematische Nachrichten》2018,291(4):699-703
This paper deals, given an arbitrary locally compact Abelian group, with the existence of integrable functions all whose convolution powers are essentially unbounded. 相似文献
7.
Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudocompact group topology, Forum Math. 6 (3) (1994) 323–337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm–Kaplansky invariants.We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan, M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811–837], and Dikranjan and Shakhmatov [D. Dikranjan, D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1–3) (2005) 2–54] showed this equivalence for groups of cardinality not greater than .We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality κω, for any infinite cardinal κ. In particular, it is consistent that for every cardinal κ there are countably compact groups without non-trivial convergent sequences whose weight λ has countable cofinality and λ>κ. 相似文献
8.
Ulrich Albrecht 《Proceedings of the American Mathematical Society》2003,131(4):1021-1029
This paper investigates the extent to which an Abelian group is determined by the homomorphism groups . A class of Abelian groups is a Fuchs 34 class if and in are isomorphic if and only if for all . Two -groups and satisfy for all groups if and only if they have the same -Ulm-Kaplansky-invariants and the same final rank. The mixed groups considered in this context are the adjusted cotorsion groups and the class introduced by Glaz and Wickless. While is a Fuchs 34 class, the class of (adjusted) cotorsion groups is not. 相似文献
9.
E. A. Gorin 《Mathematical Notes》2000,68(2):167-172
The existence of homeomorphisms establishign an isometry of normalized Haar measures on (metrizable) compact groups is studied.
In the case of 0-dimensional groups, a complete answer is given in terms of the indices of open normal subgroups. For example,
for the countable powers of the groups ℤ/(m) and ℤ/(n), the answer is affirmative if and only ifm andn have the same prime divisors. A certain class of extensions of 0-dimensional groups is also studied.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 188–194, August, 2000. 相似文献
10.
On the torus group, on the group of p-adic integers, and on the p-adic solenoid, we give a construction of an arbitrary weakly infinitely divisible probability measure using a random element
with values in a product of (possibly infinitely many) subgroups of ℝ. As a special case of our results, we have a new construction
of the Haar measure on the p-adic solenoid. 相似文献
11.
Dikran Dikranjan Michael Tkachenko 《Proceedings of the American Mathematical Society》2002,130(8):2487-2496
We prove under the assumption of Martin's Axiom that every precompact Abelian group of size belongs to the smallest class of groups that contains all Abelian countably compact groups and is closed under direct products, taking closed subgroups and continuous isomorphic images.
12.
Every pseudocompact Abelian group of uncountable weight has both a proper dense pseudocompact subgroup and a strictly finer pseudocompact group topology.
13.
Christopher Deninger 《Journal of the American Mathematical Society》2006,19(3):737-758
In 1990, Lind, Schmidt, and Ward gave a formula for the entropy of certain -dynamical systems attached to Laurent polynomials , in terms of the (logarithmic) Mahler measure of . We extend the expansive case of their result to the noncommutative setting where gets replaced by suitable discrete amenable groups. Generalizing the Mahler measure, Fuglede-Kadison determinants from the theory of group von Neumann algebras appear in the entropy formula.
14.
15.
Michael J. Mossinghoff Christopher G. Pinner Jeffrey D. Vaaler. 《Mathematics of Computation》1998,67(224):1707-1726
Given a monic real polynomial with all its roots on the unit circle, we ask to what extent one can perturb its middle coefficient and still have a polynomial with all its roots on the unit circle. We show that the set of possible perturbations forms a closed interval of length at most , with achieved only for polynomials of the form with in . The problem can also be formulated in terms of perturbing the constant coefficient of a polynomial having all its roots in . If we restrict to integer coefficients, then the polynomials in question are products of cyclotomics. We show that in this case there are no perturbations of length that do not arise from a perturbation of length . We also investigate the connection between slightly perturbed products of cyclotomic polynomials and polynomials with small Mahler measure. We describe an algorithm for searching for polynomials with small Mahler measure by perturbing the middle coefficients of products of cyclotomic polynomials. We show that the complexity of this algorithm is , where is the degree, and we report on the polynomials found by this algorithm through degree 64.
16.
Mihail Ursul 《代数通讯》2017,45(11):4817-4832
We give a complete characterization of torsion-complete and algebraically compact abelian groups whose endomorphism rings admit a compact ring topology. 相似文献
17.
Salehi and Scheidt [6] have derived several Wold-Cramér concordance theorems for q-variate stationary processes over discrete groups. In this paper we characterize the concordance of the Wold decomposition with respect to families arising in the interpolation problem and the Cramér decomposition for non-full-rank q-variate stationary processes over certain nondiscrete locally compact Abelian (LCA) groups. Moreover, we give an answer to a question of Salehi and Scheidt [6, p. 319] on a characterization of the Wold-Cramér concordance with respect to J0. As corollary we then deduce a characterization of J0-regularity. 相似文献
18.
Dikran Dikranjan 《代数通讯》2015,43(1):212-224
Using the nice properties of the w-divisible weight and the w-divisible groups, we prove a factorization theorem for compact abelian groups K; namely, K = K tor × K d , where K tor is a bounded torsion compact abelian group and K d is a w-divisible compact abelian group. By Pontryagin duality this result is equivalent to the same factorization for discrete abelian groups proved in [9]. 相似文献
19.
20.
Simon Thomas 《Journal of the American Mathematical Society》2003,16(1):233-258
We prove that for each , the classification problem for torsion-free abelian groups of rank is not Borel reducible to that for torsion-free abelian groups of rank .