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basis
Applications to constructing a basis inZ(g) for classical g are also sketched.
      
A basis is calledmonomial if each of its elements is the result of applying to a (fixed) highest weight vector a monomial in the Chevalley basis elementsYα, α a simple root, in the opposite Borel subalgebra.
      
On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al.
      
We describe a basis forY, show that it is a polynomial algebra and describe its rank, which we compute explicitly in a number of cases.
      
Our basic tool is Lusztig's canonical basis and the string parametrization of this basis.
      
In order to prove this, we compare, using the Schur duality, these elements with the Kashiwara canonical basis of an integrable module.
      
As the third application, we describe a K-basis for the ring of invariants for the adjoint action of ${\rm SL}_2(K)$ on m copies of $sl_2(K)$ in terms of traces.
      
The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimensional tilting and irreducible characters for the Lie superalgebra osp(2|2n).
      
For any ε >amp;gt; 0, we construct an orthonormal Schauder basis of C(K) consisting of trigonometric polynomials Tn n = 1, 2, .
      
We present two generalizations of the orthogonal basis of Malvar and Coifman-Meyer: biorthogonal and equal parity bases.
      
For Fourier-bandlimited symbols, we derive the expected formulae for composition and commutators and construct an orthonormal basis of common approximate eigenvectors that could be used to study spectral theory.
      
For Fourier-bandlimited symbols, we derive the expected formulae for composition and commutators and construct an orthonormal basis of common approximate eigenvectors that could be used to study spectral theory.
      
We construct a basis for each Wk, so that the entire collection is a frame for L2(dμ).
      
This wavelet basis is obtained from three wavelet generators by scaling, translation and rotation, and the wavelets are supported either by one corner triangle or a pair of adjacent triangles in the triangulation of level k - 1.
      
A new class of unbalanced haar wavelets that form an unconditional basis for Lp on general measure spaces
      
Given a complete separable σ-finite measure space (X,Σ, μ) and nested partitions of X, we construct unbalanced Haar-like wavelets on X that form an unconditional basis for Lp (X,Σ, μ) where1>amp;lt;p>amp;lt;∞.
      
We show that if(X,Σ, μ) is not purely atomic, then the unconditional basis constant of our basis is (max(p, q) -1).
      
In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis.
      
In the case of an orthonormal basis, our estimate reduces to Kadec' optimal 1/4 result.
      
We show that in this case any frame is a Riesz basis and our characterization of Riesz bases may be considered as a generalization of the theorems established by Coifman, et al.
      
 

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