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 one A wandering set for a map ? is a set containing precisely one element from each orbit of ?. For ? having at most one discontinuity, the existence of a Borel wandering set is equivalent to rationality of the Poincaré rotation number. We obtain this equality as a particular case of a more general one, which is reminiscent of a well-known identity in the stochastic calculus setting, namely the It? formula. Our approach relies on an extension of the classical Calderón-Zygmund theory of singular integral operators which allow one to consider Cauchy type operators with variable kernels on Lipschitz graphs. Specifically, for1>amp;lt;p>amp;lt;∞, we obtain sufficient conditions for the weight in one side, which guarantee that another weight exists in the other side, so that the corresponding Lp weighted inequality holds for T*. The Calderón Projector, is one of the most important tools in the study of boundary value problems for elliptic operators. This description is based on a one-to-one correspondence between the set of all solutions of the Covariance Extension Problem and the set of all contractive analytic functions H from the open unit disk with values on the space of q × q matrices. A wavelet frame is called decomposable whenever it is equivalent to a superwavelet frame of length greater than one. We discuss the linear independence of systems ofmvectors in n-dimensional complex vector spaces where the m vectors are time-frequency shifts of one generating vector. We use a different approach which allows to establish that the one-sided Sawyer Ap weights are the natural ones to study the boundedness and convergence of that series in weighted spaces. The notions of localization and related approximation properties are a spectrum of ideas that quantify the degree to which elements of one frame can be approximated by elements of another frame. The one-dimensional case is closely related to a number theoretical conjecture on tilings by Coven and Meyerowitz [1]. It is always in the Schwartz space; one can choose f so that it has all moments vanishing, or has compact support with arbitrarily many moments vanishing. The iterations, initially formulated for time-continuous Gabor systems, are considered and tested in a discrete setting in which one passes to the appropriately sampled-and-periodized windows and frame operators. The Density Theorem for Gabor Frames is one of the fundamental results of time-frequency analysis. Toeplitz operators on the Bergman space of the unit disc can be written as integrals of the symbol against an invariant operator field of rank-one projections. As a special case one obtains modulation spaces and Gabor frames on spheres. If that collection forms a frame for $\mathcal{M}$, one can introduce two different types of shift-generated (SG) dual frames for X, called type I and type II SG-duals, respectively. Demeter about the boundedness of series of difference of convolutions to the setting of one-sided Ap weights. Here Z is the standard Zak transform and g is an even, real, well-behaved window such that Zg has exactly one zero, at

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2008 CNKI－中国知网

2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社