2 research outputs found
Multivariate tile B-splines
Tile B-splines in are defined as autoconvolutions of the
indicators of tiles, which are special self-similar compact sets whose integer
translates tile the space . These functions are not
piecewise-polynomial, however, being direct generalizations of classical
B-splines, they enjoy many of their properties and have some advantages. In
particular, the precise values of the H\"older exponents of the tile B-splines
are computed in this work. They sometimes exceed the regularity of the
classical B-splines. The orthonormal systems of wavelets based on the tile
B-splines are constructed and the estimates of their exponentional decay are
obtained. Subdivision schemes constructed by the tile B-splines demonstrate
their efficiency in applications. It is achieved by means of the high
regularity, the fast convergence, and small number of the coefficients in the
corresponding refinement equation.Comment: 45 pages, 37 figure