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Lichtenstein in the caseu =(n, ?) or(n?), we prove that ?(q).ζ1/2 is non zero for all harmonic polynomialsq ∈S() \ {0}.
      
Coordinates on Schubert cells, Kostant's harmonic forms, and the Bruhat Poisson structure onG/B
      
For the flag manifoldX=G/B of a complex semi-simple Lie groupG, we make connections between the Kostant harmonic forms onG/B and the geometry of the Bruhat Poisson structure.
      
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 boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.
      
We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.
      
In this survey we study some interplay between classical complex analysis (removable sets for bounded analytic functions), harmonic analysis (singular integrals), and geometric measure theory (rectifiability).
      
Flatness of domains and doubling properties of measures supported on their boundary, with applications to harmonic measure
      
Harmonic analysis on SL(2,?) and projectively adapted pattern representation) and projectively adapted pattern representation
      
Then,SL(2, ?)-harmonic analysis, in the noncompact picture of induced representations, is used to decompose patterns into the components invariant under irreducible representations of the principal series ofSL(2, ?).
      
The projectively adapted properties of theSL(2, ?)-harmonic analysis, as applied to the problems, in image processing, are confirmed by computational tests.
      
On boundary behavior of harmonic functions in H?lder domains
      
We analyze the boundary behavior of harmonic functions in a domain whose boundary is locally given by a graph of a H?lder continuous function.
      
and study some properties of the harmonic measure.
      
Spherical harmonic series have many of the same wonderful properties as Fourier series, but have lacked one important thing: a numerically stable fast transform analogous to the Fast Fourier Transform (FFT).
      
Without a fast transform, evaluating (or expanding in) spherical harmonic series on the computer is slow-for large computations probibitively slow.
      
The convergence inL1 of singular integrals in harmonic analysis and ergodic theory
      
The classical Hecke identity gives the Fourier transform of the product of a homogeneous harmonic polynomial h times the Gaussian e-1/2>amp;lt;...>amp;gt;.
      
It is shown that there is a similar identity when the inner product is replaced by an indefinite quadratic formq and h is a Л-harmonic distribution, where Л is the differential operator canonically associated toq.
      
Double coset decompositions and computational harmonic analysis on groups
      
 

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