共查询到20条相似文献,搜索用时 31 毫秒
1.
Let p ≥ 2 be a prime number and ℤp be the ring of p-adic intergers. Let G be a semigroup generated by infinitely many contractive maps on pT 相似文献
2.
We study those functions that can be written as a finite sum of periodic integer valued functions. On ℤ we give three different
characterizations of these functions. For this we prove that the existence of a real valued periodic decomposition of a ℤ
→ ℤ function implies the existence of an integer valued periodic decomposition with the same periods. This result depends
on the representation of the greatest common divisor of certain polynomials with integer coefficients as a linear combination
of the given polynomials where the coefficients also belong to ℤ[x]. We give an example of an ℤ → {0, 1} function that has a bounded real valued periodic decomposition but does not have a
bounded integer valued periodic decomposition with the same periods. It follows that the class of bounded ℤ → ℤ functions
has the decomposition property as opposed to the class of bounded ℝ → ℤ functions. If the periods are pairwise commensurable
or not prescribed, then we get more general results.
Supported by OTKA grants T 43623 and K 61908. 相似文献
3.
A. Vourdas 《Journal of Fourier Analysis and Applications》2010,16(5):748-767
Harmonic analysis on ℤ(p
ℓ
) and the corresponding representation of the Heisenberg-Weyl group HW[ℤ(p
ℓ
),ℤ(p
ℓ
),ℤ(p
ℓ
)], is studied. It is shown that the HW[ℤ(p
ℓ
),ℤ(p
ℓ
),ℤ(p
ℓ
)] with a homomorphism between them, form an inverse system which has as inverse limit the profinite representation of the
Heisenberg-Weyl group
\mathfrak HW[\mathbbZp,\mathbbZp,\mathbbZp]\mathfrak {HW}[{\mathbb{Z}}_{p},{\mathbb{Z}}_{p},{\mathbb{Z}}_{p}]. Harmonic analysis on ℤ
p
is also studied. The corresponding representation of the Heisenberg-Weyl group HW[(ℚ
p
/ℤ
p
),ℤ
p
,(ℚ
p
/ℤ
p
)] is a totally disconnected and locally compact topological group. 相似文献
4.
Vsevolod F. Lev 《Israel Journal of Mathematics》2006,154(1):221-233
We show that ifp is prime andA is a sum-free subset of ℤ/
p
ℤ withn:=|A|>0.33p, thenA is contained in a dilation of the interval [n,p−n] (modp). 相似文献
5.
L. O. Chekhov 《Theoretical and Mathematical Physics》2006,146(1):13-24
We investigate the AdS3/CFT2 correspondence for the Euclidean AdS3 space compactified on a solid torus with the CFT field on the regularizing boundary surface in the bulk. Correlation functions
corresponding to the bulk theory at a finite temperature tend to the standard CFT correlation functions in the limit of removed
regularization. In the sum over geometries in both the regular and the ℤ
N orbifold cases, the two-point correlation function for massless modes transforms into a finite sum of products of the conformal-anticonformal
CFT Green's functions up to divergent terms proportional to the volume of the SL(2, ℤ)/ℤ group.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 17–30, January, 2006. 相似文献
6.
A. E. Troitskaya 《Journal of Mathematical Sciences》2009,159(6):879-893
Assume that Δ and Π are representations of the group ℤ2 by operators on the space L
2(X, μ) that are induced by measure-preserving automorphisms, and for some d, the representations Δ⨂d
and Π⨂d
are conjugate to each other, Δ(ℤ2
\(0, 0)) consists of weakly mixing operators, and there is a weak limit (over some subsequence in ℤ2 of operators from Δ(ℤ2)) which is equal to a nontrivial, convex linear combination of elements of Δ(ℤ2) and of the projection onto constant functions. We prove that in this case, Δ and Π are also conjugate to each other.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 193–212, 2007. 相似文献
7.
P. M. Akhmet’ev 《Journal of Mathematical Sciences》2009,159(6):761-776
We present an approach to the Kervaire-invariant-one problem. The notion of the geometric (ℤ/2 ⨁ ℤ/2)-control of self-intersection of a skew-framed immersion and the notion of the (ℤ/2 ⨁ ℤ/4)-structure on the self-intersection manifold of a D
4-framed immersion are introduced. It is shown that a skew-framed immersion ↬ℝ
n
, 0 < q ≪ n (in the -range), admits a geometric (ℤ/2 ⨁ ℤ/2)-control if the characteristic class of the skew-framing of this immersion admits a retraction of order q, i.e., there exists a mapping such that this composition → ℝP∞ is the characteristic class of the skew-framing of f. Using the notion of (ℤ/2 ⨁ ℤ/2)-control, we prove that for a sufficiently large n, n = 2
l
− 2, an arbitrarily immersed D
4-framed manifold admits in the regular cobordism class (modulo odd torsion) an immersion with a (ℤ/2 ⨁ ℤ/4)-structure.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 17–41, 2007. 相似文献
8.
The Marcinkiewicz-Zygmund inequality and the Bernstein inequality are established on ∮2m(T,R)∩L2(R) which is the space of polynomial splines with irregularly distributed nodes T={tj}j∈Z, where {tj}j∈Z is a real sequence such that {eitξ}j∈Z constitutes a Riesz basis for L2([-π,π]). From these results, the asymptotic relation E(f,Bπ,2)2=lim E(f,∮2m(T,R)∩L2(R))2 is proved, where Bπ,2 denotes the set of all functions from L2(R) which can be continued to entire functions of exponential type ≤π, i.e. the classical Paley-Wiener class. 相似文献
9.
We prove that if the existence of a supercompact cardinal is consistent with ZFC, then it is consistent with ZFC that the
p-rank of Ext
ℤ(G, ℤ) is as large as possible for every prime p and for any torsion-free Abelian group G. Moreover, given an uncountable
strong limit cardinal μ of countable cofinality and a partition of Π (the set of primes) into two disjoint subsets Π0 and Π1, we show that in some model which is very close to ZFC, there is an almost free Abelian group G of size 2μ = μ+ such that the p-rank of Ext
ℤ(G, ℤ) equals 2μ = μ+ for every p ∈ Π0 and 0 otherwise, that is, for p ∈ Π1.
Number 874 in Shelah’s list of publications. Supported by the German-Israeli Foundation for Scientific Research & Development
project No. I-706-54.6/2001.
Supported by a grant from the German Research Foundation DFG.
__________
Translated from Algebra i Logika, Vol. 46, No. 3, pp. 369–397, May–June, 2007. 相似文献
10.
Yu. V. Nagrebetskaya 《Algebra and Logic》2000,39(4):276-291
We deal with the decidability problem for first-order theories of a complete linear group GL(n,ℤ) of all integral matrices
of order n ≥ 3. and of a respective complete linear monoid ML(n,ℤ). It is proved that theories ∀? ∧ GL(3,ℤ). ∃∀∧ GL(3,ℤ).
∀? ∧ ML(3,ℤ), and ∃? ∧ ML(3,ℤ) are critical. and that ∃∀ ∧ νGL(n,ℤ) and ∃∀ ∧ML(n,ℤ) are decidable for any n ≥ 3.
Translated fromAlgebra i Logika, Vol. 39, No. 4, pp. 480–504, July–August, 2000. 相似文献
11.
Martin Avendano Teresa Krick Ariel Pacetti 《Foundations of Computational Mathematics》2006,6(1):82-120
The main result of this paper is a new version of Newton-Hensel lifting
that relates to interpolation questions. It allows one to lift polynomials in ℤ[x] from information modulo a prime number
p ≠ 2 to a power pk for any k, and its originality is that it is a mixed version that not only lifts the coefficients of the polynomial but
also its exponents. We show that this result corresponds exactly to a Newton--Hensel lifting of a system of 2t generalized
equations in 2t unknowns in the ring of p-adic integers ℤp. Finally, we apply our results to sparse polynomial interpolation in ℤ[x]. 相似文献
12.
Morten Nielsen 《Advances in Computational Mathematics》2007,27(2):195-209
Given a dilation matrix A :ℤd→ℤd, and G a complete set of coset representatives of 2π(A
−Tℤd/ℤd), we consider polynomial solutions M to the equation ∑
g∈G
M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric
polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices,
we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of
arbitrary order.
Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network. 相似文献
13.
Let C(X, ℤ), C(X, ℂ) and C(X) denote the ℓ-groups of integer-valued, rational-valued and real-valued continuous functions on a topological space X, respectively. Characterizations are given for the extensions C(X, ℤ) ⩽ C(X, ℚ) ⩽ C(X) to be rigid, major, and dense. 相似文献
14.
We prove that for almost allσ ∈G ℚ the field
has the following property: For each absolutely irreducible affine varietyV of dimensionr and each dominating separable rational mapϕ:V→
there exists a point a ∈
such thatϕ(a) ∈ ℤr. We then say that
is PAC over ℤ. This is a stronger property then being PAC. Indeed we show that beside the fields
other fields which are algebraic over ℤ and are known in the literature to be PAC are not PAC over ℤ. 相似文献
15.
T. Sanders 《Journal d'Analyse Mathématique》2007,101(1):123-162
The paper has two main parts. To begin with, suppose that G is a compact abelian group. Chang’s Theorem can be viewed as a structural refinement of Bessel’s inequality for functions
ƒ ∈ L
2(G). We prove an analogous result for functions ƒ ∈ A(G), where A(G) is the space
endowed with the norm
, and generalize this to the approximate Fourier transform on Bohr sets.
As an application of the first part of the paper, we improve a recent result of Green and Konyagin. Suppose that p is a prime number and A ⊂ ℤ/pℤ has density bounded away from 0 and 1 by an absolute constant. Green and Konyagin have shown that ‖χ
A
‖
A(ℤ/pℤ) ≫ ɛ (log p)1/3−ɛ; we improve this to ‖χ
A
‖
A(ℤ/pℤ) ≫ ɛ (log p)1/2−ɛ. To put this in context, it is easy to see that if A is an arithmetic progression, then ‖χ
A
‖
A(ℤ/pℤ) ≪ log p. 相似文献
16.
Abdelmalek Azizi 《Rendiconti del Circolo Matematico di Palermo》1999,48(1):71-92
Let ℕ,i=√−1,k=ℚ(√d,i) andC
2 the 2-part of the class group ofk. Our goal is to determine alld such thatC
2⋍ℤ/2ℤ×ℤ/2ℤ.
Soientd∈ℕ,i=√−1,k=ℚ(√d,i), etC
2 la 2-partie du groupe de classes dek. On s'intéresse à déterminer tous lesd tel queC
2⋍ℤ/2ℤ×ℤ/2ℤ.
相似文献
17.
We examine iteration graphs of the squaring function on the rings ℤ/nℤ when n = 2
k
p, for p a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric
when k = 3 and when k ⩾ 5 and are symmetric when k = 4. 相似文献
18.
Umberto Zannier 《Archiv der Mathematik》1997,68(2):129-138
Let/e fєℤ[x, y] be an absolutely irreducible polynomial. A classical result by Ostrowski states that the reduction modulo p of f remains absolutely irreducible for all large prime numbers p. Here we give a new sufficient condition on p for the conclusion to hold. The result, which holds for polynomials defined over arbitrary discrete valuation rings, also
implies equality of the genera of the curves defined by f and its reduction. The method of proof stems from Hensel’s principle and analytic continuation of p-adic analytic functions, following Dwork and Robba. 相似文献
19.
Éric Balandraud 《Israel Journal of Mathematics》2012,188(1):405-429
Using the polynomial method in additive number theory, this article establishes a new addition theorem for the set of subsums
of a set satisfying A ∩ (−A) = ∅ in ℤ/pℤ:
$\left| {\Sigma (A)} \right| \geqslant \min \{ p,1 + \tfrac{{|A|(|A| + 1)}}
{2}\} .$\left| {\Sigma (A)} \right| \geqslant \min \{ p,1 + \tfrac{{|A|(|A| + 1)}}
{2}\} . 相似文献
20.
A key tool in recent advances in understanding arithmetic progressions and other patterns in subsets of the integers is certain
norms or seminorms. One example is the norms on ℤ/Nℤ introduced by Gowers in his proof of Szemerédi’s Theorem, used to detect uniformity of subsets of the integers. Another
example is the seminorms on bounded functions in a measure preserving system (associated to the averages in Furstenberg’s
proof of Szemerédi’s Theorem) defined by the authors. For each integer k ≥ 1, we define seminorms on ℓ∞(ℤ) analogous to these norms and seminorms. We study the correlation of these norms with certain algebraically defined sequences,
which arise from evaluating a continuous function on the homogeneous space of a nilpotent Lie group on a orbit (the nilsequences).
Using these seminorms, we define a dual norm that acts as an upper bound for the correlation of a bounded sequence with a
nilsequence. We also prove an inverse theorem for the seminorms, showing how a bounded sequence correlates with a nilsequence.
As applications, we derive several ergodic theoretic results, including a nilsequence version of the Wiener-Wintner ergodic
theorem, a nil version of a corollary to the spectral theorem, and a weighted multiple ergodic convergence theorem. 相似文献
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