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1.
It is shown that irreducible finite state, Markov shifts of the same entropy and period arefinitarily isomorphic. 相似文献
2.
Two invertible dynamical systems (X, gA, μ, T) and (Y, ℬ, ν, S), where X, Y are metrizable spaces and T, S are homeomorphisms on X and Y, are said to be finitarily orbit equivalent if there exists an invertible measure preserving mapping ϕ from a subset X
0 of X of full measure to a subset Y
0 of Y of full measure such that ϕ|x
0 is continuous in the relative topology on X
0, ϕ
−1|Y
0 is continuous in the relative topology on Y
0 and ϕ(Orb
T
(x)) = Orb
Sϕ
(x) for μ-a.e. x ∈ X. In this article a finitary orbit equivalence mapping is shown to exist between any two irreducible Markov chains. 相似文献
3.
Robert M. Beals Joseph L. Wetherell Michael E. Zieve 《Israel Journal of Mathematics》2009,172(1):93-117
We develop a conditional entropy theory for infinite measure preserving actions of countable discrete amenable groups with
respect to a σ-finite factor. This includes ‘infinite’ analogues of relative Kolmogorov-Sinai, Rokhlin and Krieger theorems
on generating partitions, Pinsker theorem on disjointness, Furstenberg decomposition and disjointness theorems, etc. In case
of ℤ-action, our concept of relative entropy matches well the ‘absolute’ entropy h
Kr introduced by Krengel. Answering in part his question and a question of Silva and Thieullen, we show that for any non-distal
transformation S there exists an infinite measure preserving transformation T with h
Kr(T × S) = ∞ but h
Kr(T) = 0.
This project was supported in part by a CRDF grant UM1-2546-KH-03. 相似文献
4.
Ergodic homeomorphisms T and S of Polish probability spaces X and Y are evenly Kakutani equivalent if there is an orbit equivalence ϕ: X
0 → Y
0 between full measure subsets of X and Y such that, for some A ⊂ X
0 of positive measure, ϕ restricts to a measurable isomorphism of the induced systems T
A
and S
ϕ(A). The study of even Kakutani equivalence dates back to the seventies, and it is well known that any two irrational rotations
of the circle are evenly Kakutani equivalent. But even Kakutani equivalence is a purely measurable relation, while systems
such as irrational rotations are both measurable and topological. 相似文献
5.
We give general conditions on a generator of a C0-semigroup (resp. of a C0-resolvent) on Lp(E,μ), p ≥ 1, where E is an arbitrary (Lusin) topological space and μ a σ-finite measure on its Borel σ-algebra, so that it generates a sufficiently
regular Markov process on E. We present a general method how these conditions can be checked in many situations. Applications to solve stochastic differential
equations on Hilbert space in the sense of a martingale problem are given.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
6.
J. William Helton Daniel P. McAllaster Joshua A. Hernandez 《Integral Equations and Operator Theory》2008,61(1):77-102
The paper introduces a notion of the Laplace operator of a polynomial p in noncommutative variables x = (x
1,…, x
g
). The Laplacian Lap[p, h] of p is a polynomial in x and in a noncommuting variable h. When all variables commute we have Lap[p, h] = h
2Δ
x
p where Δ
x
p is the usual Laplacian. A symmetric polynomial in symmetric variables will be called harmonic if Lap[p, h] = 0 and subharmonic if the polynomial q(x, h) := Lap[p, h] takes positive semidefinite matrix values whenever matrices X
1,…, X
g
, H are substituted for the variables x
1,…, x
g
, h. In this paper we classify all homogeneous symmetric harmonic and subharmonic polynomials in two symmetric variables. We
find there are not many of them: for example, the span of all such subharmonics of any degree higher than 4 has dimension
2 (if odd degree) and 3 (if even degree). Hopefully, the approach here will suggest ways of defining and analyzing other partial
differential equations and inequalities.
Dedicated to Israel Gohberg on the occasion of his 80th birthday.
All authors were partially supported by J.W. Helton’s grants from the NSF and the Ford Motor Co. and J. A. Hernandez was supported
by a McNair Fellowship. 相似文献
7.
Stephen C. Preston 《Annals of Global Analysis and Geometry》2012,41(3):281-305
In this article, we study geometric aspects of the space of arcs parameterized by unit speed in the L
2 metric. Physically, this corresponds to the motion of a whip, and it also arises in studying shape recognition. The geodesic
equation is the nonlinear, nonlocal wave equation η
tt
= ∂
s
(σ η
s
), with
\lvert hs\rvert o 1{\lvert \eta_{s}\rvert\equiv 1} and σ given by
sss- \lvert hss\rvert2 s = -\lvert hst\rvert2{\sigma_{ss}- \lvert \eta_{ss}\rvert^2 \sigma = -\lvert \eta_{st}\rvert^2}, with boundary conditions σ(t, 1) = σ(t, −1) = 0 and η(t, 0) = 0. We prove that the space of arcs is a submanifold of the space of all curves, that the orthogonal projection exists
but is not smooth, and as a consequence we get a Riemannian exponential map that is continuous and even differentiable but
not C
1. This is related to the fact that the curvature is positive but unbounded above, so that there are conjugate points at arbitrarily
short times along any geodesic. 相似文献
8.
Simon [J. Approxim. Theory,
127, 39–60 (2004)] proved that the maximal operator σα,κ,* of the (C, α)-means of the Walsh–Kaczmarz–Fourier series is bounded from the martingale Hardy space H
p
to the space L
p
for p > 1 / (1 + α), 0 < α ≤ 1. Recently, Gát and Goginava have proved that this boundedness result does not hold if p ≤ 1 / (1 + α). However, in the endpoint case p = 1 / (1 + α ), the maximal operator σα,κ,* is bounded from the martingale Hardy space H
1/(1+α) to the space weak- L
1/(1+α). The main aim of this paper is to prove a stronger result, namely, that, for any 0 < p ≤ 1 / (1 + α), there exists a martingale f ∈ H
p
such that the maximal operator σα,κ,*
f does not belong to the space L
p
. 相似文献
9.
Ya. G. Sinai 《Commentarii Mathematici Helvetici》1985,60(1):173-178
We consider two commuting automorphismsT
1,T
2 of the Lebesque space (M, M, μ) such thath
m,n=h(T
1
m
T
2
n
)<∞ whereh is the measure-theoretic entropy. Under additional assumptions we show the existence of the limits lim (1/m)h
m,n wherem→∞,n→∞,m/n→ω and ω is an irrational number. 相似文献
10.
LetX be a Riemann surface of genusg. The surfaceX is called elliptic-hyperelliptic if it admits a conformal involutionh such that the orbit spaceX/〈h〉 has genus one. The involutionh is then called an elliptic-hyperelliptic involution. Ifg>5 then the involutionh is unique, see [A]. We call symmetry to any anticonformal involution ofX. LetAut
±(X) be the group of conformal and anticonformal automorphisms ofX and letσ, τ be two symmetries ofX with fixed points and such that {σ, hσ} and {τ, hτ} are not conjugate inAut
±(X). We describe all the possible topological conjugacy classes of {σ, σh, τ, τh}. As consequence of our study we obtain that, in the moduli space of complex algebraic curves of genusg (g even >5), the subspace whose elements are the elliptic-hyperelliptic real algebraic curves is not connected. This fact contrasts
with the result in [Se]: the subspace whose elements are the hyperelliptic real algebraic curves is connected.
The authors are supported by BFM2002-04801. 相似文献
11.
H. Stetkær 《Aequationes Mathematicae》1997,54(1-2):144-172
Summary We produce complete solution formulas of selected functional equations of the formf(x +y) ±f(x + σ (ν)) = Σ
I
2
=1
g
l
(x)h
l
(y),x, y∈G, where the functionsf,g
1,h
1 to be determined are complex valued functions on an abelian groupG and where σ:G→G is an involution ofG. The special case of σ=−I encompasses classical functional equations like d’Alembert’s, Wilson’s first generalization of it, Jensen’s equation and
the quadratic equation. We solve these equations, the equation for symmetric second differences in product form and similar
functional equations for a general involution σ. 相似文献
12.
LetX
1 andX
2 be two mixing Markov shifts over finite alphabet. If the entropy ofX
1 is strictly larger than the entropy ofX
2, then there exists a finitary homomorphism ϕ:X
1→X
2 such that the code length is anL
p
random variable for allp<4/3. In particular, the expected length of the code ϕ is finite.
Research supported by KBN grant 2 P03A 039 15 1998–2001. 相似文献
13.
Let E = Eσ : y2 = x(x + σp)(x + σq) be elliptic curves, where σ = ±1, p and q are primenumbers with p+2 = q. (i) Selmer groups S(2)(E/Q), S(φ)(E/Q), and S(φ)(E/Q) are explicitly determined,e.g. S(2)(E+1/Q)= (Z/2Z)2, (Z/2Z)3, and (Z/2Z)4 when p ≡ 5, 1 (or 3), and 7(mod 8), respectively. (ii)When p ≡ 5 (3, 5 for σ = -1) (mod 8), it is proved that the Mordell-Weil group E(Q) ≌ Z/2Z Z/2Z,symbol, the torsion subgroup E(K)tors for any number field K, etc. are also obtained. 相似文献
14.
H.G. Rotstein et al. proposed a nonconserved phase-field system characterized by the presence of memory terms both in the heat conduction and
in the order parameter dynamics. These hereditary effects are represented by time convolution integrals whose relaxation kernels
k and h are nonnegative, smooth and decreasing. Rescaling k and h properly, we obtain a system of coupled partial integrodifferential equations depending on two relaxation times ɛ and σ.
When ɛ and σ tend to 0, the formal limiting system is the well-known nonconserved phase-field model proposed by G. Caginalp.
Assuming the exponential decay of the relaxation kernels, the rescaled system, endowed with homogeneous Neumann boundary conditions,
generates a dissipative strongly continuous semigroup Sɛ, σ(t) on a suitable phase space, which accounts for the past histories of the temperature as well as of the order parameter. Our
main result consists in proving the existence of a family of exponential attractors
for Sɛ, σ(t), with ɛ, σ ∈ [0, 1], whose symmetric Hausdorff distance from
tends to 0 in an explicitly controlled way. 相似文献
15.
Kazem Ghanbari 《Positivity》2006,10(4):721-729
We denote the spectrum of an square matrix A by σ(A), and that of the matrix obtained by deleting the first i rows and columns of A by σi(A). It is known that a symmetric pentadiagonal oscillatory (SPO) matrix may be constructed from σ, σ1 and σ2. The pairs σ, σ1 and σ1, σ2 must interlace; the construction is not unique; and the conditions on the data which ensure that A is oscillatory are extremely complicated. Given one SPO matrix A, the paper shows that operations may be applied to A to construct a family of such matrices with σ and σ1 in common. Moreover, given one totally positive (TP) matrix A, we construct a family of TP matrices with σ, σ1 and σ2 in common. 相似文献
16.
Jérôme Buzzi 《Israel Journal of Mathematics》1997,100(1):125-161
We generalize the technique of Markov Extension, introduced by F. Hofbauer [10] for piecewise monotonic maps, to arbitrary
smooth interval maps. We also use A. M. Blokh’s [1] Spectral Decomposition, and a strengthened version of Y. Yomdin’s [23]
and S. E. Newhouse’s [14] results on differentiable mappings and local entropy.
In this way, we reduce the study ofC
r
interval maps to the consideration of a finite number of irreducible topological Markov chains, after discarding a small
entropy set. For example, we show thatC
∞ maps have the same properties, with respect to intrinsic ergodicity, as have piecewise monotonic maps. 相似文献
17.
Zhiting Xu 《Monatshefte für Mathematik》2007,150(2):157-171
Some oscillation criteria are established by the averaging technique for the second order neutral delay differential equation
of Emden-Fowler type
where x(t) = y(t) + p(t)y(t − τ), τ, σ1 and σ2 are nonnegative constants, α > 0, β > 0, and a, p, q
1,
. The results of this paper extend and improve some known results. In particular, two interesting examples that point out
the importance of our theorems are also included. 相似文献
18.
Walter Parry 《Israel Journal of Mathematics》1992,77(3):265-271
The following theorem is proven. LetM be a closed, orientable, irreducible 3-manifold such that rankH
1(M, ℤ/pℤ)≥3 for some primep. Then either π1(M) is virtually solvable or it contains a free group of rank 2. 相似文献
19.
Denote by B
2σ,p
(1 < p < ∞) the bandlimited class p-integrable functions whose Fourier transform is supported in the interval [−σ, σ]. It is shown that a function in B
2σ,p
can be reconstructed in L
p(ℝ) by its sampling sequences {f (κπ / σ)}
κ∈ℤ and {f’ (κπ / σ)}
κ∈ℤ using the Hermite cardinal interpolation. Moreover, it will be shown that if f belongs to L
p
r
(ℝ), 1 < p < ∞, then the exact order of its aliasing error can be determined.
Project supported by the Scientific Research Common Program of Beijing Municipal Commission of Education under grant number
KM 200410009010 and by the Natural Science Foundation of China under grant number 10071006 相似文献
20.
K. Kubilius 《Lithuanian Mathematical Journal》1999,39(3):251-261
The uniform distance between the solution of a nonlinear equation driven by a functionh with boundedp-variation and its Milstein-type approximation is estimated by δ
n
v γ
p
(n) v γ
p
2
(n), where δ
n
=max(t
k
−t
k−1
) is the maximum step size of the approximation on the interval [0,T], γ
p
(n)=max υ
p
1/p
(h;[t
k-1,t
k
]), 1 <p < 2, and υ
p
(h;[t
k-1,t
k
]) is thep-variation of the functionh on [t
k-1,t
k]. In particular, ifh is a Lipschitz function of order α, then the uniform distance has the bound δ
n
α
for δn <1.
Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius; Vilnius Technical University, Saulétekio 11, 2054 Vilnius,
Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 317–330, July–September, 1999. 相似文献