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1.
Ryotaro Sato 《Proceedings of the American Mathematical Society》2003,131(1):231-233
Let be an ergodic automorphism of a probability measure space and let be a real-valued measurable function on . We deduce a necessary and sufficient condition for the existence of -solutions of the cohomology equation , by using the recent result of Alonso, Hong and Obaya.
2.
Francisco Brito 《代数通讯》2013,41(20):2277-2297
3.
M. Lemanczyk F. Parreau D. Volný 《Transactions of the American Mathematical Society》1996,348(12):4919-4938
Given an irrational rotation, in the space of real bounded variation functions it is proved that there are ergodic cocycles whose small perturbations remain ergodic; in fact, the set of ergodic cocycles has nonempty dense interior.
Given a pseudo-homogeneous Banach space and an irrational rotation, we study the set of elements satisfying the mean ergodic theorem. Once such a space is not homogeneous, we prove it is not reflexive and not separable. In ``natural" cases, up to -cohomology, the only elements satisfying the mean ergodic theorem are those from the closure of trigonometric polynomials.
For pseudo-homogeneous spaces admitting a Koksma's inequality ergodicity of the corresponding cylinder flows can be deduced from spectral properties of some circle extensions. In particular this is the case of Lebesgue spectrum (in the orthocomplement of the space of eigenfunctions) for the circle extension.
4.
Kai TAO 《Frontiers of Mathematics in China》2012,7(3):521-542
It is known that the Lyapunov exponent is not continuous at certain points in the space of continuous quasi-periodic cocycles.
We show that the Lyapunov exponent is continuous for a higher-dimensional analytic category in this paper. It has a modulus
of continuity of the form exp(−∣logt∣
σ
) for some 0 < σ < 1. 相似文献
5.
We characterize those homogeneous polynomials P [z1, ... ,zd] for which the principal ideal (P) = P · A(d) is complementedin A(d) or, equivalently, those which admit a continuous lineardivision operator. The condition is the same as that which characterizes,among the homogeneous polynomials, those which are nonellipticand for which P(D) is surjective in A(d), and those for whichP(D) admits a continuous linear right inverse in C(d). It dependsonly on the type of real singularities. 相似文献
6.
J.M. Almira 《Applied Mathematics Letters》2012,25(6):1016-1018
7.
We prove that the Lyapunov exponent of quasi-periodic cocycles with singularities behaves continuously over the analytic category. We thereby generalize earlier results, where singularities were either excluded completely or constrained by additional hypotheses. Applications include parameter dependent families of analytic Jacobi operators, such as extended Harper’s model describing crystals in varying lattice geometries subject to external magnetic fields. 相似文献
8.
Marja Kankaanrinta 《Topology and its Applications》2012,159(5):1489-1496
Let X be a real analytic orbifold. Then each stratum of X is a subanalytic subset of X. We show that X has a unique subanalytic triangulation compatible with the strata of X. We also show that every Cr-orbifold, 1?r?∞, has a real analytic structure. This allows us to triangulate differentiable orbifolds. The results generalize the subanalytic triangulation theorems previously known for quotient orbifolds. 相似文献
9.
Adam W. Strzebongraveski 《代数通讯》2013,41(1):41-50
In this paper we eliminate the complex analytic part from original Lojasiewicz's proof and show a constructive method of producing a saucissonnage for a set of polynomials. 相似文献
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Fernando Cobos Luz M. Fernández-Cabrera Thomas Kühn Tino Ullrich 《Journal of Functional Analysis》2009,256(7):2321-3722
We investigate the limit class of interpolation spaces that comes up by the choice θ=0 in the definition of the real method. These spaces arise naturally interpolating by the J-method associated to the unit square. Their duals coincide with the other extreme spaces obtained by the choice θ=1. We also study the behavior of compact operators under these two extreme interpolation methods. Moreover, we establish some interpolation formulae for function spaces and for spaces of operators. 相似文献
13.
Explicit examples of smooth cocycles not cohomologous to constants are constructed. Necessary and sufficient conditions on
the irrational numberθ are given for the existence of such cocycles. It is shown that, depending onθ, the set ofC
r cocycles whose skew-product is ergodic is either residual or empty. 相似文献
14.
Tejinder S. Neelon 《Proceedings of the American Mathematical Society》1997,125(9):2531-2535
Analyticity of solutions , of systems of real analytic equations , is studied. Sufficient conditions for and power series solutions to be real analytic are given in terms of iterative Jacobian ideals of the analytic ideal generated by . In a special case when the 's are independent of , we prove that if a solution satisfies the condition , then is necessarily real analytic.
15.
Xiaonan Ma 《Israel Journal of Mathematics》2002,131(1):1-50
In this paper, we prove the functoriality of the analytic torsion forms of Bismut and Lott [BLo] with respect to the composition
of two submersions. 相似文献
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We characterize the Liouvillian and analytic integrability of the quadratic polynomial vector fields in R2 having an invariant ellipse.More precisely,a quadratic system having an invariant ellipse can be written into the form x=x2+y2-1+y(ax+by+c),y=x(ax+by+c),and the ellipse becomes x2+y2=1.We prove that(i) this quadratic system is analytic integrable if and only if a=0;(ii) if x2+y2=1 is a periodic orbit,then this quadratic system is Liouvillian integrable if and only if x2+y2=1 is not a limit cycle;and(iii) if x2+y2=1 is not a periodic orbit,then this quadratic system is Liouvilian integrable if and only if a=0. 相似文献
18.
In this note we completely describe the structure of algebraic semigroups S with Sx=S or Sx degenerate and xS=S or xS degenerate
for each x∈S. We then apply our results in characterizing the separately continuous multiplications on a topological space
whose only self-maps are either surjective or have degenerate image. In particular, we find that any locally compact Hausdorff
space with this property can admit only trivial separately continuous multiplications. Examples of spaces satisfying this
property are certain continua discovered by H. Cook [1]. The authors are indebted to Karl H. Hofmann and James T. Rogers for
conversations elucidating the topological implications of Theorem 1.
The second author supported by NSF Grant GP28655 相似文献
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20.
D. E. Papush 《Journal of Mathematical Sciences》1990,48(2):196-201
Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 43, pp. 93–98, 1985. 相似文献