Reiterated ergodic algebras and applicat
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Reiterated ergodic algebras and applicat
Reiterated ergodic algebras and applicat
Commun. Math. Phys. 300,835-876(2010)Digital Object Identifier (DOI) 10.1007/s0ơ220-0l0-l 127-3Communications inMathematical PhysicsReiterated Ergodic Reiterated ergodic algebras and applicat c Algebras and ApplicationsGabriel Nguetseng1, Mamadou Sango2. Jean Louis Woukeng2 31 Department of Mathematics. University of Yaounde I, P.O. Box 812. Yaounde. Cameroon.E-mail: nguctscng@uyl.uninct.cm- Department of Mathematics and Applied Mathematics. University of Pretoria. Pretoria 0002. South A Reiterated ergodic algebras and applicat frica.E-mail: mamadou.sango@up.ac.za' Department of Mathematics and Computer Science. University of Dschang. P.O. Box 67. Dschang.Cameroon. E-mail: j\Reiterated ergodic algebras and applicat
voukcng@yahoo.fr; jcanlouis.woukcng@up.ac.zaReceived: 13 February 2010/Accepted: 17 April 2010Published online: 6 September 2010 - & springer-Verlag 2Commun. Math. Phys. 300,835-876(2010)Digital Object Identifier (DOI) 10.1007/s0ơ220-0l0-l 127-3Communications inMathematical PhysicsReiterated Ergodic Reiterated ergodic algebras and applicat We show that this enables one to treat more complicated homogenization problems than those solved by the previous theory. In particular we exhibit an example of algebra which, contrary to the algebra of almost periodic functions, induces no homogenization algebra. We prove some general compactness Reiterated ergodic algebras and applicat results which are then applied to the resolution of some homogenization problems related to the generalized Reynolds type equations and to some nonlinReiterated ergodic algebras and applicat
ear hyperbolic equations.1IntroductionA homogenization algebra (//-algebra, in short) is any separable Banach subalgebra of the algebra of bounded conCommun. Math. Phys. 300,835-876(2010)Digital Object Identifier (DOI) 10.1007/s0ơ220-0l0-l 127-3Communications inMathematical PhysicsReiterated Ergodic Reiterated ergodic algebras and applicat pt has been the starting point of a recent theory developed by the first author [26]: the deterministic homogenization theory. The basic result of this theory is stated as follows.Theorem 1.1. Any bounded sequence (ue)£QE in LP(Q) (1 < p < 00 and E being an ordinary' sequence) admits a subsequence w Reiterated ergodic algebras and applicat hich is weakly RZ-convergent.The proof of this result is based fundamentally on the separability of the //-algebra A considered. In 2002, in the frameReiterated ergodic algebras and applicat
work of the theory of algebras with mean value introduced by Zhikov and Krivenko 133]. Casado and Gayte [11] proved Theorem 1.1 without resorting to tCommun. Math. Phys. 300,835-876(2010)Digital Object Identifier (DOI) 10.1007/s0ơ220-0l0-l 127-3Communications inMathematical PhysicsReiterated Ergodic Reiterated ergodic algebras and applicat the following result.Theorem 1.2. Let X be a subspace (not necessarily closed) of a reflexive Banach space Y and let fn : X -> ]R be a sequence of linear functionals (not necessarily continuous).836G. Nguctscng. M. Sango. J. L. WoukcngAssume there exists a constant c > 0 such thatlimsup/ní.v) < c|| Reiterated ergodic algebras and applicat .v|| for all X e X. n-1.1Then there exist a subsequence (fnk)k of (fn) and a functional f e Y' such that \ỉmkfnk(x) - f(x)forallx e X.A thorough analyReiterated ergodic algebras and applicat
sis of the proof of this result allows to realize that there is implicitly a certain positive assumption on the functionals /„. which makes the resultCommun. Math. Phys. 300,835-876(2010)Digital Object Identifier (DOI) 10.1007/s0ơ220-0l0-l 127-3Communications inMathematical PhysicsReiterated Ergodic Reiterated ergodic algebras and applicat acing in (1.1). /rt(-r) by |./n(.v)|. Here we show that if in Theorem 1.2 we replace " fti{x)" by “|/M(x)| ” and “ fn : X —> R" by “ flt : X -» C”, we obtain the conclusion of this theorem without much change to the proof presented by Casado and Gayte. The result we get is of a very wide applicabili Reiterated ergodic algebras and applicat ty for both nonlinear problems (whose operators are generally real coefficients) and linear problems (whose operators are generally complex coefficienReiterated ergodic algebras and applicat
ts).More precisely, in this paper we revisit the theory of H-algebras. We show that the separability assumption is unnecessary. This allows one to ideCommun. Math. Phys. 300,835-876(2010)Digital Object Identifier (DOI) 10.1007/s0ơ220-0l0-l 127-3Communications inMathematical PhysicsReiterated Ergodic Reiterated ergodic algebras and applicat apart from the algebra of perturbed almost periodic functions) no H -algebra, as has always been the case for the algebra of almost periodic functions.The paper is organized as follows. In Sect. 2 we state the simplified form of H-algebra (without the separability assumption) which we call the H -su Reiterated ergodic algebras and applicat pralgebra. We show that all the existing properties of the framework of H-algebras are still valid in our context. In Sect. 3 we collect and prove a fReiterated ergodic algebras and applicat
ew general compactness results. Finally in Sects. 4 and 5. we apply the results of the earlier sections to the resolution of two homogenization probleCommun. Math. Phys. 300,835-876(2010)Digital Object Identifier (DOI) 10.1007/s0ơ220-0l0-l 127-3Communications inMathematical PhysicsReiterated Ergodic Reiterated ergodic algebras and applicat ramework of reiterated homogenization theory.Unless otherwise specified, vector spaces throughout are assumed to be complex vector spaces, and scalar functions are assumed to take complex values. We shall always assume that the numerical space R"'' (integer m > 1) and its open sets are each provided Reiterated ergodic algebras and applicat with the Lebesgue measure dx = dxị .. .dxm. also denoted by À. For those concepts regarding integration theory, we refer to [6.7].2Homogenization SupReiterated ergodic algebras and applicat
ralgebras2.1.Homogenization supralgebras. We use a new concept of homogenization algebras. It is more general than the previous one by the first authoCommun. Math. Phys. 300,835-876(2010)Digital Object Identifier (DOI) 10.1007/s0ơ220-0l0-l 127-3Communications inMathematical PhysicsReiterated Ergodic Reiterated ergodic algebras and applicat ollowing two actions of R* (the multiplicative group of positive real numbers) on the numerical space (d = A' or in), defined as follows:H,(x) = — (X e R*'),H,(x) = — (.veR"‘).Í2-2.1 Reiterated ergodic algebras and applicat Commun. Math. Phys. 300,835-876(2010)Digital Object Identifier (DOI) 10.1007/s0ơ220-0l0-l 127-3Communications inMathematical PhysicsReiterated ErgodicGọi ngay
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