Multivariate tile $\mathrm{B}$-splines
چکیده
Tile $\mathrm{B}$-splines in $\mathbb R^d$ are defined as autoconvolutions of indicators tiles, which special self-similar compact sets whose integer translates tile the space R^d$. These functions not piecewise-polynomial, however, being direct generalizations classical $\mathrm{B}$-splines, they enjoy many their properties and have some advantages. In particular, exact values Hölder exponents evaluated shown, cases, to exceed those $\mathrm{B}$-splines. Orthonormal systems wavelets based on B-splines constructed, estimates exponential decay obtained. Efficiency applications is demonstrated an example subdivision schemes surfaces. This efficiency achieved due high regularity, fast convergence, small number coefficients corresponding refinement equation.