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As a consequence, the action is linearizable if certain topological conditions are satisfied.
      
An algebraicG-varietyX is called "wonderful", if the following conditions are satisfied:X is (connected) smooth and complete;X containsr irreducible smoothG-invariant divisors having a non void transversal intersection;G has 2r orbits inX.
      
Here we provide certain conditions (more general than those in [Ka1]) which guarantee preservation of the topology under a modification.
      
We express the vanishing conditions satisfied by the correlation functions of Drinfeld currents of quantum affine algebras, imposed by the quantum Serre relations.
      
We discuss the relation of these vanishing conditions with a shuffle algebra description of the algebra of Drinfeld currents.
      
Moreover we give some conditions so thatF*(?[t1,...,tn-1]) is the ring of invariants of φ.
      
Representations of the exceptional lie superalgebraE(3, 6) I: Degeneracy conditions
      
We also give conditions for the two algebras to be equal, relating equality to good filtrations and saturated subgroups.
      
More precisely, we show that under some conditions on X, every such automorphism is of the form Φ = ?g, where ? is an algebraic action of a linear algebraic group G of dimension 1 on X, and where g belongs to G.
      
We investigate conditions on kernel operators in order to provide prescribed orders of approximation in the Triebel-Lizorkin spaces.
      
The present work presents conditions on ? for which the transform relation holds in the classical sense, and extends this result to a class of generalizations of the Poisson formula in any number of dimensions.
      
Orthogonality conditions for ?1, …, ?q naturally impose constraints on the scaling coefficients, which are then called the wavelet matrix.
      
Furthermore, we generalize the sufficient and necessary conditions of orthogonality given by Lawton and Cohen to the case of several dimensions and arbitrary dilation matrix A.
      
The admissibility conditions for the wavelet measure μ are presented in terms of μ itself and in terms of the Fourier transform of μ.
      
Sharp inequalities between weight bounds (from the doubling, Ap, and reverse H?lder conditions) and the BMO norm are obtained when the former are near their optimal values.
      
We present weak sufficient conditions for decay of a wavelet so that the wavelet basis is an unconditional basis in Lp(?), 1 >amp;lt;p >amp;lt; ∞.
      
If the sequence of functions ?j, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions.
      
We are interested in finding necessary and sufficient conditions for irregular sampling to hold.
      
Further we investigate under which conditions one can replace the discrete model of the finite section method by the periodic discrete model, which is used in many numerical procedures.
      
In this paper we give a comprehensive set of necessary and sufficient conditions for the orthogonality of compactly supported refinable functions and refinable function vectors.
      
 

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