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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 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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