Wavelets with Complementary Boundary Conditions — Function Spaces on the Cube

Wavelets with Complementary Boundary Conditions — Function Spaces on the Cube
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具有互补边界条件的小波 — 立方体上的函数空间

DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
R. Schneider
R. Schneider
中科院分区：
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文献类型：
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作者：
W. Dahmen;R. Schneider

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本文研究了n维立方体上的双正交小波基的构造，它为Sobolev空间和Besov空间提供了Riesz基，且在任意的边界面上具有齐次Dirichlet边界条件.其实质是原始小波和对偶小波满足相应的互补边界条件。这些结果形成的关键成分的建设小波基流形[DS2]已开发的治疗算子方程的积极和消极的顺序。
This paper is concerned with the construction of biorthogonal wavelet bases on n-dimensional cubes which provide Riesz bases for Sobolev and Besov spaces with homogeneous Dirichlet boundary conditions on any desired selection of boundary facets. The essential point is that the primal and dual wavelets satisfy corresponding complementary boundary conditions. These results form the key ingredients of the construction of wavelet bases on manifolds [DS2] that have been developed for the treatment of operator equations of positive and negative order.