共查询到10条相似文献,搜索用时 240 毫秒
1.
The main goal of this paper is to understand which properties of a basis are important for certain direct and inverse theorems
in nonlinear approximation. We study greedy approximation with regard to bases with different properties. We consider bases
that are tensor products of univariate greedy bases. Some results known for unconditional bases are extended to the case of
quasi-greedy bases. 相似文献
2.
Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual Riesz bases of compactly supported wavelets. We give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions, and we present a sufficient conditions for the decay of their Fourier transforms. We study the regularity of these biorthogonal bases. We provide several families of examples, all symmetric (corresponding to “linear phase” filters). In particular we can construct symmetric biorthogonal wavelet bases with arbitraily high preassigned regularity; we also show how to construct symmetric biorthogonal wavelet bases “close” to a (nonsymmetric) orthonormal basis. 相似文献
3.
Dorin Ervin Dutkay Gabriel Picioroaga Myung-Sin Song 《Journal of Mathematical Analysis and Applications》2014
We show how some orthonormal bases can be generated by representations of the Cuntz algebra; these include Fourier bases on fractal measures, generalized Walsh bases on the unit interval and piecewise exponential bases on the middle third Cantor set. 相似文献
4.
A. I. Zobnin 《Journal of Mathematical Sciences》2008,152(4):522-539
We generalize Hoon Hong’s theorem on Gröbner bases under composition to the case of differential standard bases in the ordinary ring of differential polynomials {ie4152-01}. In particular, we prove that some ideals have finite differential standard bases. We construct special orderings on differential monomials such that ideals generated by some power of a quasi-linear polynomial acquire finite differential standard bases. 相似文献
5.
Serkan Ho?ten 《Journal of Combinatorial Theory, Series A》2007,114(2):311-321
We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is greater than a computable bound, the Markov bases consist of elements from Markov bases of smaller tables. We give an explicit formula for this bound in terms of Graver bases. We also compute these Markov and Graver complexities for all K×2×2×2 tables. 相似文献
6.
We construct
2-graded crystal bases for the quantized universal enveloping algebra of the Lie superalgebraosp(1, 2r). We show that, like the crystal bases in the Lie algebra case, these crystal bases carry a remarkable combinatorial structure. 相似文献
7.
We construct polynomial orthonormal bases in various function spaces. Our bases have linear order of growth of degrees of
polynomials. We show that this order is optimal. 相似文献
8.
9.
We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types.Under the specialization of q and coefficients to 1,these bases are generic bases of finite and affine cluster algebras. 相似文献
10.
We investigate biorthogonal Wilson bases generated by cardinal B-splines. Such bases provide very efficient representations of sinusoids modulated by spline functions. Exact Riesz bounds for such bases are given. Furthermore, we derive an explicit formula for the computation of the dual window functions and determine their decay rates. 相似文献