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We show that on each Schubert cell, the corresponding Kostant harmonic form can be described using only data coming from the Bruhat Poisson structure.
      
We study and compare their approximation properties and applicability in data compression.
      
We show that global well-posedness occurs even when the initial data is rough.
      
The main goal is to develop the corresponding theory for Lp-integrable bounday data for optimal values of p's.
      
A class of fast orthogonal transformations for finite strings of data are described.
      
The method we use is a combination of the smoothing effect of the operator ?t + ?x(2j+1) and a gauge transformation performed on a linear system, which allows us to consider initial data with arbitrary size.
      
A fundamental problem with the DWT, however, is the treatment of finite length data sequences.
      
Commonly used techniques such as circular convolution and symmetric extension can produce undesirable edge effects which propagate into the interior of the transformed data as the number of DWT iterations increases.
      
Well-posedness of a semilinear heat equation with weak initial data
      
In the first part the initial value problem (IVP) of the semilinear heat equation with initial data in is studied.
      
We prove the well-posedness when and construct non-unique solutions for In the second part the well-posedness of the avove IVP for k=2 with μ0?Hs(?n) is proved if and this result is then extended for more general nonlinear terms and initial data.
      
The problem of reconstruction of the function from the data of its integrals over half circles A ? H with centers at the diameter of H is studied.
      
For example, we study Plemelj-Calderón-Seeley-Bojarski type splittings of Cauchy boundary data into traces of 'inner' and 'outer' monogenics and show that this problem has finite index.
      
Two subdivision schemes with Hermite data on ? are studied.
      
These schemes use 2 or 7 parameters respectively depending on whether Hermite data involve only first derivatives or include second derivatives.
      
Microlocal Analysis of an FBP Algorithm for Truncated Spiral Cone Beam Data
      
We prove in two dimensions that the set of Cauchy data for the Pauli Hamiltonian
      
We consider the Camassa-Holm equation with data in the energy norm H1(R1).
      
At the end of the article, the method is tested on real magnetic field data measured by the German geoscientific research satellite CHAMP.
      
We give a sufficient condition on finite data of lengthm, or step functions determined on the intervals [k/m, (k + 1)/m) , k = 0,...,m - 1 of [0, 1), to be written as a Riesz-type product in terms of the rows of H(m).
      
 

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