共查询到20条相似文献,搜索用时 734 毫秒
1.
Christophe Dupont 《Mathematische Annalen》2011,349(3):509-528
Let f be an endomorphism of
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} and ν be an f-invariant measure with positive Lyapunov exponents (λ
1, . . . , λ
k
). We prove a lower bound for the pointwise dimension of ν in terms of the degree of f, the exponents of ν and the entropy of ν. In particular our result can be applied for the maximal entropy measure μ. When k = 2, it implies that the Hausdorff dimension of μ is estimated by dimHm 3 [(log d)/(l1)] + [(log d)/(l2)]{{\rm dim}_\mathcal{H}\mu \geq {{\rm log} d \over \lambda_1} + {{\rm log} d \over \lambda_2}}, which is half of the conjectured formula. Our method for proving these results consists in studying the distribution of
the ν-generic inverse branches of f
n
in
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} . Our tools are a volume growth estimate for the bounded holomorphic polydiscs in
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} and a normalization theorem for the ν-generic inverse branches of f
n
. 相似文献
2.
3.
The concept of enlargement of a generalized topology was introduced by á. Császár [4]. He also introduced the concepts of
(κ,λ)-continuity and (κ
μ
,λ
ν)-continuity on enlargements. In this paper, we characterize the (κ,λ)-continuity and introduce the concept of strong (κ,λ)-continuity on enlargements. In particular, we study characterizations for the strong (κ,λ)-continuity and the relationships among (μ,ν)-continuity, (κ,λ)-continuity, strong (κ,λ)-continuity and (κ
μ
,λ
ν)-continuity. 相似文献
4.
Given a sequence of measures (μ
n
) on a topological semigroupS, a measure λ onS is called a tail limit of (μ
n
) if for some subsequence of integers (n
i
),
converges weakly to ν
k
for allk and λ is a weak limit point of the sequence (ν
k
). The main theorem of this paper characterizes the supports of the tail limits on compact completely simple semigroups. Some
applications of the theorem and various open problems are discussed. 相似文献
5.
We show that for certain self-similar measures μ with support in the interval 0≤x≤1, the analytic functions {e
i2πnx
:n=0,1,2, …} contain an orthonormal basis inL
2 (μ). Moreover, we identify subsetsP ⊂ ℕ0 = {0,1,2,...} such that the functions {e
n
:n ∈ P} form an orthonormal basis forL
2 (μ). We also give a higher-dimensional affine construction leading to self-similar measures μ with support in ℝ
ν
, obtained from a given expansivev-by-v matrix and a finite set of translation vectors. We show that the correspondingL
2 (μ) has an orthonormal basis of exponentialse
i2πλ·x
, indexed by vectors λ in ℝ
ν
, provided certain geometric conditions (involving the Ruelle transfer operator) hold for the affine system.
Work supported by the National Science Foundation. 相似文献
6.
Yosef Stein 《Israel Journal of Mathematics》1989,68(1):109-122
LetK be an algebraically closed field of characteristic zero. ForA ∈K[x, y] let σ(A) = {λ ∈K:A − λ is reducible}. For λ ∈ σ(A) letA − λ = ∏
i=1
n(λ)
A
iλ
k
μ whereA
iλ are distinct primes. Let ϱλ(A) =n(λ) − 1 and let ρ(A) = Σλɛσ(A)ϱλ(A). The main result is the following:
Theorem.If A ∈ K[x, y] is not a composite polynomial, then ρ(A) < degA. 相似文献
7.
Jumela F. Sarmiento 《Graphs and Combinatorics》2002,18(3):621-632
A t(v,k,λ) design is a set of v points together with a collection of its k-subsets called blocks so that t points are contained in exactly λ blocks. PG(n,q), the n-dimensional projective geometry over GF(q) is a 2(q
n
+q
n−1
+⋯+q+1,q
2+q+1, q
n−2
+ q
n−3
+⋯+q+1) design when we take its points as the points of the design and its planes as the blocks of the design. A 2(v,k,λ) design is said to be resolvable if the blocks can be partitioned as ℱ={R
1,R
2,…,R
s
}, where s=λ(v−1)/(k−1) and each R
i
consists of v/k disjoint blocks. If a resolvable design has an automorphism σ which acts as a cycle of length v on the points and ℱσ=ℱ, then the design is said to be point-cyclically resolvable. The design consisting of points and planes of PG(5,2) is shown to be point-cyclically resolvable by enumerating all inequivalent
resolutions which are invariant under a cyclic automorphism group G=〈σ〉 where σ is a cycle of length v. These resolutions are shown to be the only resolutions which admit point-transitive automorphism group.
Received: November 10, 1999 Final version received: September 18, 2000
Acknowledgments. The author would like to thank A. Munemasa for his assistance in writing computer programs on constructing projective spaces
and searching for partial spreads. Moreover, she's thankful to T. Hishida and M.␣Jimbo for helpful discussions and for verifying
the results of this paper.
Present address: Mathematics Department, Ateneo de Manila University, Loyola Heights, Quezon City 1108, Philippines. e-mail: jumela@mathsci.math.admu.edu.ph 相似文献
8.
Jian Wang 《高校应用数学学报(英文版)》2008,23(3):345-350
A K1,k-factorization of λKm,n is a set of edge-disjoint K1,k-factors of λKm,n, which partition the set of edges of λKm,n. In this paper, it is proved that a sufficient condition for the existence of K1,k-factorization of λKm,n, whenever k is any positive integer, is that (1) m ≤ kn, (2) n ≤ km, (3) km-n = kn-m ≡ 0 (mod (k^2- 1)) and (4) λ(km-n)(kn-m) ≡ 0 (mod k(k- 1)(k^2 - 1)(m + n)). 相似文献
9.
James Olsen 《Israel Journal of Mathematics》1972,11(1):1-13
The principal result of this paper is that the convex combination of two positive, invertible, commuting isometries ofL
p(X,F, μ) 1<p<+∞, one of which is periodic, admits a dominated estimate with constantp/p−1. In establishing this, the following analogue of Linderholm’s theorem is obtained: Let σ and ε be two commuting non-singular
point transformations of a Lebesgue Space with τ periodic. Then given ε>O, there exists a periodic non-singular point transformation σ′ such that σ′ commutes with τ and μ(x:σ′x≠σx}<ε. Byan approximation argument, the principal result is applied to the convex combination of two isometries ofL
p (0, 1) induced by point transformations of the form τx=x
k,k>0 to show that such convex combinations admit a dominated estimate with constantp/p−1.
Research supported in part by NSF Grant No. GP-7475. A portion of the contents of this paper is based on the author’s doctoral
dissertation written under the direction of Professor R. V. Chacon of the University of Minnesota. 相似文献
10.
W. G. Bridges 《Israel Journal of Mathematics》1972,12(4):369-372
Bounds on the number of row sums in ann×n, non-singular (0,1)-matrixA sarisfyingA
tA=diag (k
1-λ1,…,k
n-λn),k
j>λj>0,λ1=…=λe,λe+1=…=λn are obtained which extend previous results for such matrices. 相似文献
11.
12.
We develop a theory of “special functions” associated with a certain fourth-order differential operator Dm,n\mathcal{D}_{\mu,\nu} on ℝ depending on two parameters μ,ν. For integers μ,ν≥−1 with μ+ν∈2ℕ0, this operator extends to a self-adjoint operator on L
2(ℝ+,x
μ+ν+1 dx) with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive
basic properties of the eigenfunctions such as orthogonality, completeness, L
2-norms, integral representations, and various recurrence relations. 相似文献
13.
Kh. Kh. Ruzimuradov 《Journal of Mathematical Sciences》1996,79(5):1320-1324
Let Λ be a unimodular lattice in ℝ2, μ a homogeneous minimum of Λ; let P(a,b)⊂ℝ2 be a rectangle with vertices at the points (a,0), ...(0,b), P(a, b)+X its image under the translation by a vector X ∈ ℝ2. We prove that there exists a sequence of positive numbers v1<v2<...<vk<... with
, such that for u>μ the rectangle P(u, vk)+X contains T=S(P)+R points of Λ, where |R|<5; here S(P) is the area of the rectangle. Bibliography: 4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 82–89.
Translated by O. A. Ivanov. 相似文献
14.
Won Keun Min 《Acta Mathematica Hungarica》2011,132(4):339-347
We introduce the notion of mixed weak (μ,ν1ν2)-continuity between a generalized topology μ and two generalized topologies ν1, ν2. We characterize such continuity in terms of mixed generalized open sets: (ν1,ν2)′-semiopen sets, (ν1,ν2)′-preopen sets, (ν1,ν2)-preopen sets [2], (ν1,ν2)′-β′-open sets and θ(ν1,ν2)-open sets [3]. In particular, we show that for a given mixed weakly (μ,ν1ν2)-continuous function, if the codomain of the given function is mixed regular (=(ν1,ν2)-regular), then the function is also (μ,ν1)-continuous. 相似文献
15.
Let λ and μ be solid sequence spaces. For a sequence of modulus functions Φ = (ϕ k) let λ(Φ) = {x = (x
k
): (ϕk(|x
k
|)) ∈ λ}. Given another sequence of modulus functions Ψ = (ψk), we characterize the continuity of the superposition operators P
f
from λ(Φ) into μ (Ψ) for some Banach sequence spaces λ and μ under the assumptions that the moduli ϕk (k ∈ ℕ) are unbounded and the topologies on the sequence spaces λ(Φ) and μ(Ψ) are given by certain F-norms. As applications
we consider superposition operators on some multiplier sequence spaces of Maddox type.
This research was supported by Estonian Science Foundation Grant 5376. 相似文献
16.
17.
A. F. Ramírez 《Probability Theory and Related Fields》1998,110(3):369-395
Summary. Let η be a diffusion process taking values on the infinite dimensional space T
Z
, where T is the circle, and with components satisfying the equations dη
i
=σ
i
(η) dW
i
+b
i
(η) dt for some coefficients σ
i
and b
i
, i∈Z. Suppose we have an initial distribution μ and a sequence of times t
n
→∞ such that lim
n
→∞μS
tn
=ν exists, where S
t
is the semi-group of the process. We prove that if σ
i
and b
i
are bounded, of finite range, have uniformly bounded second order partial derivatives, and inf
i
,ησ
i
(η)>0, then ν is invariant.
Received: 12 September 1996 / In revised form: 10 November 1997 相似文献
18.
P. M. Edwards 《Semigroup Forum》1989,39(1):257-262
For a congruence σ on a semigroupS a congruence μ(σ) onS, containing σ, is defined such that the semigroupS/σ is fundamental if and only if σ=μ(σ). The congruence μ(σ) is shown to possess maximality properties and for idempotent-surjective
semigroups, μ(σ) is the maximum congruence with respect to the partition of the idempotents determined by σ. Thus μ is the
maximum idempotent-separating congruence on any idempotent-surjective semigroup. It is shown that μ(μ(σ))=μ(σ).
If ρ is another congruence onS, possibly with the same partition of the idempotents as σ, then it is of interest to know when ρ⊆σ (or ρ⊆μ(σ)) implies μ(ρ)⊆μ(σ)
or even μ(ρ)=μ(σ). These implications are not true in general but if σ⊆ρ⊆μ(σ) then μ(ρ)⊆μ(σ). IfS is an idempotent-surjective semigroup and ρ and σ have the same partition of the idempotents then μ(ρ)=μ(σ). 相似文献
19.
Tetsutaro Shibata 《Journal d'Analyse Mathématique》1995,66(1):277-294
The nonlinear two-parameter Sturm-Liouville problemu
"+μg(u)=λf(u) is studied for μ, λ>0. By using Ljusternik-Schnirelman theory on the general level set developed by Zeidler, we shall show
the existence of ann-th variational eigenvalue λ=λn(μ). Furthermore, for specialf andg, the asymptotic formula of λ1(μ)) as μ→∞ is established. 相似文献
20.
Jorge J. Betancor Juan C. Fariña Teresa Martinez Lourdes Rodríguez-Mesa 《Arkiv f?r Matematik》2008,46(2):219-250
In this paper we investigate Riesz transforms R
μ
(k) of order k≥1 related to the Bessel operator Δμ
f(x)=-f”(x)-((2μ+1)/x)f’(x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We
obtain that for every k≥1, R
μ
(k) is a principal value operator of strong type (p,p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ(x)=x
2μ+1
dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R
μ
(k) maps L
p
(ω) into itself and L
1(ω) into L
1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman. 相似文献