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- W4313197344 abstract "Tile B-splines in $mathbb{R}^d$ are defined as autoconvolutions of the indicators of tiles, which are special self-similar compact sets whose integer translates tile the space $mathbb{R}^d$. 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 Holder 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." @default.
- W4313197344 created "2023-01-06" @default.
- W4313197344 creator A5024458645 @default.
- W4313197344 date "2022-12-25" @default.
- W4313197344 modified "2023-09-27" @default.
- W4313197344 title "Multivariate tile B-splines" @default.
- W4313197344 doi "https://doi.org/10.48550/arxiv.2212.12945" @default.
- W4313197344 hasPublicationYear "2022" @default.
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