Abstract
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.
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Dedicated to P.L. Butzer on the occasion of his 70th birthday
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Dahmen, W., Schneider, R. Wavelets with Complementary Boundary Conditions — Function Spaces on the Cube. Results. Math. 34, 255–293 (1998). https://doi.org/10.1007/BF03322055
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DOI: https://doi.org/10.1007/BF03322055