Fractional cone and hex splines
| Autor: | Peter Massopust, Patrick J. Van Fleet |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
$s$-dimensional mesh
Box spline 65D07 General Mathematics 010102 general mathematics Mathematical analysis box splines fractional and complex B-splines 020206 networking & telecommunications Geometry 02 engineering and technology 01 natural sciences Mathematics::Numerical Analysis Computer Science::Graphics Cone (topology) Cone splines hex splines 0202 electrical engineering electronic engineering information engineering 0101 mathematics (fractional) difference operator 41A15 42A38 Mathematics |
| Zdroj: | Rocky Mountain J. Math. 47, no. 5 (2017), 1655-1691 |
| Popis: | We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain $s$-directional meshes and include as special cases the $3$-directional box splines~\cite {article:condat} and hex splines~\cite {article:vandeville} previously considered by Condat and Van De Ville, et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex B-splines defined in~\cite {article:fbu, article:ub} and, e.g., investigated in~\cite {article:fm, article:mf}. Explicit time domain representations are de\-rived for these splines on $3$-directional meshes. We present some properties of these two multivariate spline families, such as recurrence, decay and refinement. Finally, we show that a bivariate hex spline and its integer lattice translates form a Riesz basis of its linear span. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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