共查询到20条相似文献,搜索用时 15 毫秒
1.
S. R. Foguel 《Israel Journal of Mathematics》1964,2(3):198-200
We consider, in this note, some invariant subspaces of a unitary operator induced by a measure preserving transformation. For these subspaces two problems are studied:
- a.Is the subspace generated by characteristic functions? 相似文献
2.
G. Boole proved that the transformation φ of the real line, defined by φ(x)=x−1/x, preserves Lebesgue measure. A general method is applied to proving that φ is ergodic. Some further applications of the method
are also indicated. 相似文献
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For a measure preserving transformation \(T\) of a probability space \((X,\mathcal{F },\mu )\) and some \(d \ge 1\) we investigate almost sure and distributional convergence of random variables of the form $$\begin{aligned} x \rightarrow \frac{1}{C_n} \sum _{0\le i_1,\ldots ,\,i_d where \(C_1, C_2,\ldots \) are normalizing constants and the kernel \(f\) belongs to an appropriate subspace in some \(L_p(X^d\!,\, \mathcal{F }^{\otimes d}\!,\,\mu ^d)\) . We establish a form of the individual ergodic theorem for such sequences. Using a filtration compatible with \(T\) and the martingale approximation, we prove a central limit theorem in the non-degenerate case; for a class of canonical (totally degenerate) kernels and \(d=2\) , we also show that the convergence holds in distribution towards a quadratic form \(\sum _{m=1}^{\infty } \lambda _m\eta ^2_m\) in independent standard Gaussian variables \(\eta _1, \eta _2, \ldots \) . 相似文献
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6.
H. Rindler 《Mathematische Annalen》1988,279(3):403-412
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9.
Peter D. Lax 《纯数学与应用数学通讯》1971,24(2):133-135
10.
Matthew Foreman 《Topology and its Applications》2010,157(8):1404-1414
Many recent results about the classification problem for ergodic measure preserving transformations involve global considerations about spaces of measure preserving transformations. This paper surveys recent joint work with Dan Rudolph and Benjamin Weiss in determining when various spaces of measure preserving transformations are equivalent in the sense of conjugacy preserving Borel isomorphism and in having the same generic dynamical properties. 相似文献
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12.
I. A. Yurov 《Mathematical Notes》1998,63(6):823-836
Let {a
n
}
n
=0/
be a uniformly distributed sequence ofp-adic integers. In the present paper we study continuous functions close to differentiable ones (with respect to thep-adic metric); for these functions, either the sequence {f(a
n
)}
n
=0/
is uniformly distributed over the ring ofp-adic integers or, for all sufficiently largek, the sequences {f
k
(k(an))}
n
=0/
are uniformly distributed over the residue class ring modp
k
, where
k
is the canonical epimorphism of the ring ofp-adic integers to the residue class ring modp
k
andf
k
is the function induced byf on the residue class ring modp
k
(i.e.,f k
(x)
=f(
k
(x)) (modp
k
)). For instance, these functions can be used to construct generators of pseudorandom numbers.Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 935–950, June, 1998.In conclusion, the author wishes to express his deep gratitude to V. S. Anashin for permanent attention to this research and for support. 相似文献
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14.
Each set E ⊂ ℕ is realized as the set of essential values of the multiplicity function of the Koopman operator for an ergodic conservative
infinite measure preserving transformation. 相似文献
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17.
Alexandre I. Danilenko 《Israel Journal of Mathematics》2018,228(1):21-51
We introduce concepts of Radon MSJ and Radon disjointness for infinite Radon measure preserving homeomorphisms of the locally compact Cantor space. We construct an uncountable family of pairwise Radon disjoint infinite Chacon like transformations. Every such transformation is Radon strictly ergodic, totally ergodic, asymmetric (not isomorphic to its inverse), has Radon MSJ and possesses Radon joinings whose ergodic components are not joinings. 相似文献
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19.
A family of infinite measure preserving odometers is presented which exhibit examples ofp-recurrent but notp+1-recurrent ergodic transformations for everyp>1. 相似文献
20.
We construct a conservative ergodic transformation of the real line whose normalised Birkhoff sums are distributionally generic.
This proves that distributional genericity is itself generic. 相似文献