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1.
2.
Schwartz's almost periodic distributions are generalized to the case of Banach space valued distributions , and furthermore for a given arbitrary class A to for φ∈ test functions D(R,C)}. It is shown that this extension process is iteration complete, i.e. . Moreover the T from are characterized in various ways, also tempered distributions with P={X-valued functions of polynomial growth} are shown. Under suitable assumptions , , where for all h>0}, is defined with the corresponding extension of Mh. With an extension of the indefinite integral from to D′(R,X) a distribution analogue to the Bohl-Bohr-Amerio-Kadets theorem on the almost periodicity of bounded indefinite integrals of almost periodic functions is obtained, also for almost automorphic, Levitan almost periodic and recurrent functions, similar for a result of Levitan concerning ergodic indefinite integrals. For many of the above results a new (Δ)-condition is needed, we show that it holds for most of the A needed in applications. Also an application to the study of asymptotic behavior of distribution solutions of neutral integro-differential-difference systems is given. 相似文献
3.
A. M. Vershik 《Journal of Mathematical Sciences》1985,28(5):667-674
One presents a new variant of the theory of periodic approximations of dynamical systems and C*-algebras, namely the construction for each automorphism of the Lebesgue space of a Markov tower (or adic model) of periodic automorphisms. One gives several examples.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 115, pp. 72–82, 1982. 相似文献
4.
A. Böttcher 《Integral Equations and Operator Theory》1999,33(3):253-272
LetAP
+
(R
n
) denote the Banach algebra of all continuous almost periodic functions onR
n
whose Bohr-Fourier spectrum is contained in an additive semi-group [0, )
n
. We show that the maximal ideal space ofAP
+
(R
n
) may have a nonempty corona and we characterize all for which the corona is empty. Analogous results are established for algebras of almost periodic functions with absolutely convergent Fourier series. 相似文献
5.
L. I. Ronkin 《Ukrainian Mathematical Journal》1990,42(8):976-987
An analog of Jessen's theorem on the existence of a Jessen function and its relation to the distribution of roots of a holomorphic almost periodic function in a strip is obtained for almost periodic maps.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1094–1107, August, 1990. 相似文献
6.
We show that if (S(t))
t≧0 is a contraction semigroup on a closed convex subset of a uniformly convex Banach space, then every bounded and “asymptotically
isometric” almost-orbit of (S(t))
t≧0 is weakly almost periodic in the sense of Eberlein. As one consequence, results on the existence of almost periodic solutions
to the abstract Cauchy problem are obtained without the need fora priori compactness assumptions. As a further consequence, the known strong ergodic limit theorems for (almost-) orbits of nonlinear
contraction semigroups turn out to be special cases of Eberlein’s classical ergodic theorem for weakly almost periodic functions. 相似文献
7.
Generalized almost periodic solutions and ergodic properties of quasi-autonomous dissipative systems
Alain Haraux 《Journal of Differential Equations》1983,48(2):269-279
Let H be a real Hilbert space, A a maximal monotone operator in H and a measurable function which is S1-almost periodic. Assuming that the positive trajectories of the equation are bounded (in H) for t ? 0, we construct a kind of generalized almost periodic “solution” of the equation, and we show how to deduce information of ergodic type on the asymptotic behavior of the trajectories as t → +∞. 相似文献
8.
Motivated by a renewed interest in generalizations of classical almost periodicity (originally due to Harald Bohr), we develop
a theorem of Bochner within the framework of almost periodic functions in the sense of Stepanov. As a result we establish
some conditions that guarantee the existence of Stepanov almost periodic solutions to differential equations with Stepanov
almost periodic coefficients. Finally, we extend a now classic theorem of Favard originally stated for classical almost periodic
functions to the Stepanov almost periodic case.
相似文献
9.
LetT be a weakly almost periodic (WAP) representation of a locally compact Σ-compact groupG by linear operators in a Banach spaceX, and letM = M(T) be its ergodic projection onto the space of fixed points (i.e.,Mx is the unique fixed point in the closed convex hull of the orbit ofx). A sequence of probabilities Μn is said toaverage T [weakly] if ∫T(t)x dΜ
n converges [weakly] toM(T)x for eachx ∃X. We callΜ
n [weakly]unitarily averaging if it averages [weakly] every unitary representation in a Hilbert space, and [weakly]WAPRaveraging if it averages [weakly] every WAP representation. We investigate some of the relationships of these notions, and connect
them with properties of the regular representation (by translations) in the spaceWAP(G).
Research partially supported by the Israel Science Foundation. 相似文献
10.
Let (Ω,f,P) be a probability space and letT be a measure-preserving weak mixing transformation. We define a large class of sequences of integers calledp-sequences, such that iff∈L
1 there exists a set Ω′⊂Ω of probability one and for ω∈Ω′ we have
for everyp-sequence {kn}. 相似文献
11.
In this paper, we give a new proof of a result of R. Jones showing almost everywhere convergence of spherical means of actions of Rd on Lp(X)-spaces are convergent for d?3 and p>d/(d-1). 相似文献
12.
13.
The Bohl-Bohr-Amerio-Kadets theorem states that the indefinite integral y=Pφ of an almost periodic (ap) is again ap if y is bounded and the Banach space X does not contain a subspace isomorphic to c0. This is here generalized in several directions: Instead of it holds also for φ defined only on a half-line , instead of ap functions abstract classes with suitable properties are admissible, can be weakened to φ in some “mean” class , then ; here contains all f∈L1loc with in for all h>0 (usually strictly); furthermore, instead of boundedness of y mean boundedness, y in some , or in , ergodic functions, suffices. The Loomis-Doss result on the almost periodicity of a bounded Ψ for which all differences Ψ(t+h)−Ψ(t) are ap for h>0 is extended analogously, also to higher order differences. Studying “difference spaces” in this connection, we obtain decompositions of the form: Any bounded measurable function is the sum of a bounded ergodic function and the indefinite integral of a bounded ergodic function. The Bohr-Neugebauer result on the almost periodicity of bounded solutions y of linear differential equations P(D)y=φ of degree m with ap φ is extended similarly for ; then provided, for example, y is in some with U=L∞ or is totally ergodic and, for the half-line, Reλ?0 for all eigenvalues P(λ)=0. Analogous results hold for systems of linear differential equations. Special case: φ bounded and Pφ ergodic implies Pφ bounded. If all Reλ>0, there exists a unique solution y growing not too fast; this y is in if , for quite general . 相似文献
14.
S. R. Foguel 《Israel Journal of Mathematics》1966,4(1):11-22
Most of the material in Sections 4-5-6-8-11 has been published in [4]-[10]. We shall deal with the asymptotical behavior of
the iterates of a Markov transition function. Our aim is to generalize the results about the ‘cyclic’ convergence of the iterates
of a Markov matrix. Throughout the paper functional analytic methods are used and not probabilistic arguments. The report
is self contained, modulo standart results from functional analysis, except for the decomposition into conservative and dissipative
parts. Also we assume the existence of an invariant σ finite measure on the conservative part. This has been proved, under
some restrictions, by several authors using probabilistic methods.
The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR
66-18, through the European Office of Aerospace Research (OAR) United States Air Force. 相似文献
15.
Karl Petersen 《Journal d'Analyse Mathématique》1988,51(1):228-244
Research supported in part by NSF Grants DMS-8400730 and DMS-8620132. 相似文献
16.
Karl Petersen 《Journal d'Analyse Mathématique》1990,55(1):297-297
The online version of the original article can be found at 相似文献
17.
《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》1997,33(6):797-815
We consider the question of uniform convergence in the multiplicative ergodic theorem
相似文献
18.
J. A. Ball Yu. I. Karlovich L. Rodman I. M. Spitkovsky 《Integral Equations and Operator Theory》1998,32(3):243-281
Sarason interpolation and Toeplitz corona problems are studied for almost periodic matrix functions. Recent results on almost periodic factorization and related generalized Toeplitz operators are the main tools in the study.Supported in part by NSF Grant DMS 9500912Supported in part by NATO Collaborative Research Grant 950332Supported by NSF Grant DMS 9500924 相似文献
19.
I. V. Podvigin 《Siberian Mathematical Journal》2010,51(6):1125-1130
We prove the martingale ergodic theorem of Kachurovskii which unifies ergodic theorems and theorems on the convergence of
martingales, without using the previously required additional integrability condition for the supremum of the process. This
condition is replaced by the commutation condition on the conditional expectation and ergodic averaging operators, which for
automorphisms is equivalent to the invariance condition on the filtration; meanwhile, the unification remains valid. 相似文献
20.
Radu-Nicolae Gologan 《Proceedings of the American Mathematical Society》2000,128(5):1377-1380
Using a version of an ergodic lemma due to Cuculescu and Foias, we prove a pointwise ergodic theorem for -contractions which can be viewed as a perturbed version of the celebrated ergodic theorem of Chacon and Ornstein. Surprisingly, to some extent, the complex part of the iterates involved have no effect on the ergodic convergence.