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Gindikin that complex analytic objects related to these domains will provide explicit realizations of unitary representations ofH?.
      
Here we provide certain conditions (more general than those in [Ka1]) which guarantee preservation of the topology under a modification.
      
We investigate conditions on kernel operators in order to provide prescribed orders of approximation in the Triebel-Lizorkin spaces.
      
We provide a direct computational proof of the known inclusion ${\cal H}({\bf R} \times {\bf R}) \subseteq {\cal H}({\bf R}^2),$ where ${\cal H}({\bf R} \times {\bf R})$ is the product Hardy space defined for example by R.
      
The space spanned by the translates of φv can only provide approximation order if the refinement maskP has certain particular factorization properties.
      
We use these unitary operators to provide an interesting class of scaling functions.
      
Here we provide methods for construucting explicit examples of these sets.
      
We furthermore provide a necessary and sufficient condition for a band-limited function g(t) generating a Weyl-Heisenberg frame for L2 (?) to have a band-limited minimal dual γ0 (t).
      
We provide an almost sure convergent expansion of fractional Brownian motion in wavelets which decorrelates the high frequencies.
      
The wavelets fill in the gaps and provide the necessary high frequency corrections.
      
This somewhat technical result does provide a method for simple constructions of low pass filters whose only smoothness assumption is a Holder condition at the origin.
      
Again we provide explicit estimates for the speed of convergence.
      
These examples have an interpretation in the setting of radial functions on Rd and zonal functions on compact two-point homogeneous spaces, where they provide a new transform which possesses many properties of the classical Gabor transform.
      
Such bases provide very efficient representations of sinusoids modulated by spline functions.
      
We provide a general method to derive Banach frames and atomic decompositions for these Banach spaces by sampling the continuous frame.
      
We also provide two sufficient and verifiable conditions for a nondecreasing function to be the spectral function of a singular Sturm Liouville operator.
      
We concentrate on studying algorithms that provide expansions into a series.
      
In addition, we provide a method of construction of dimension functions.
      
We also review spherical wavelet analyses that independently provide evidence for dark energy, an exotic component of our Universe of which we know very little currently.
      
Also, we provide the reader with a simple method and a fast algorithm for finding the closed forms of the discrete deconvolvers with minimal supports that constitute exact solutions of the DMDP.
      
 

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