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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 wellknown identity in the stochastic calculus setting, namely the It? formula.


Our approach relies on an extension of the classical CalderónZygmund 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 onetoone 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 ndimensional complex vector spaces where the m vectors are timefrequency shifts of one generating vector.


We use a different approach which allows to establish that the onesided 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 onedimensional 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 timecontinuous Gabor systems, are considered and tested in a discrete setting in which one passes to the appropriately sampledandperiodized windows and frame operators.


The Density Theorem for Gabor Frames is one of the fundamental results of timefrequency 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 rankone 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 shiftgenerated (SG) dual frames for X, called type I and type II SGduals, respectively.


Demeter about the boundedness of series of difference of convolutions to the setting of onesided Ap weights.


Here Z is the standard Zak transform and g is an even, real, wellbehaved window such that Zg has exactly one zero, at

