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Reductive group actions on affine quadrics with 1-dimensional quotient: Linearization when a linear model exists
      
We investigate the eigenvalue problem for such systems and the correspondingD-module when the eigenvalues are in generic position.
      
In the interesting case when the group is of Coxeter typeDn (n≥4) we use higher polarization operators introduced by Wallach.
      
We classify all instances when a parabolic subgroupP ofG acts on its unipotent radicalPu, or onpu, the Lie algebra ofPu, with only a finite number of orbits.
      
In the course of the proof we show that one can reduce the study of generating semi-invariants to the case when the quiver has no oriented paths of length greater than one.
      
Taking a specific determination of its argument and studying its limit when approaching the Shilov boundary, we are able to define a ?-valued,G-invariant kernel for triples of mutually transversal points inS.
      
Furthermore, in the case when G is a semisimple group of adjoint
      
When the characteristic of k is 0, it is known that the invariants of d vectors, d ≥ n, are obtained from those of n vectors by polarization.
      
This result is not true when char k = p >amp;gt; 0 even in the case where H is a torus.
      
When one expands a Schur function in terms of the irreducible characters of the symplectic (or orthogonal) group, the coefficient of the trivial character is 0 unless the indexing partition has an appropriate form.
      
When a function does not belong to such a space, the sampling series may converge, not to the object function but to an "alias" of it, and an aliasing error is said to occur.
      
When coupled with the Poisson Summation formula, these results become applicable to the theory of Weyl-Heisenberg systems, in the form of lattice sum
      
Scales of quasi-norms are defined for the coefficients of the expansion that characterize, via Littlewood-Paley-Stein theory, when a radial distribution belongs to a Triebel-Lizorkin or Besov space.
      
When a = 1, b = 0 = c, the famous Whittaker-Shannon-Kotel'nikov sampling theorem is obtained as a special case.
      
We show that global well-posedness occurs even when the initial data is rough.
      
A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener's algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means.
      
A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener's algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means.
      
We prove a trigonometric inequality of Ingham's type for nonharmonic Fourier series when the gap condition between frequencies does not hold any more.
      
In this article we consider the question when one can generate a Weyl- Heisenberg frame for l2(?) with shift parameters N, M-1 (integer N, M) by sampling a Weyl-Heisenberg frame for L2(?) with the same shift parameters at the integers.
      
It is shown that this is possible when the window g ε L2(?) generating the Weyl-Heisenberg frame satisfies an appropriate regularity condition at the integers.
      
 

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