论文标题
B-Spline Quarklets和Biorthoconal多波武器
B-Spline Quarklets and Biorthogonal Multiwavelets
论文作者
论文摘要
我们表明，B-Spline Quarks和相关的夸克适合Biorthosonal多波武器理论。夸克向量用于定义子空间的序列$ v_ {p，j} $的$ l_ {2}（\ mathbb {r}）$，该$几乎满足了多项解决分析的所有条件。在某些特殊条件下，他们甚至满足所有这些属性。此外，我们证明夸克和夸克具有调制矩阵，可满足完美的重建条件。此外，我们还显示了广义的双夸克和夸克的存在，这些夸克和夸克至少是从$ \ mathcal {s}'（\ Mathbb {r}）$的至少紧凑的钢化分布。最后，我们还验证了夸克和夸克可以用来定义子空间的序列$ w_ {p，j} $ $ l_ {2}（\ Mathbb {r}）$产生$ l_ {2}（2}（\ Mathbb {r}）$的非正交分解的$ l_ {2}（\ Mathbb {r}）$。
We show that B-spline quarks and the associated quarklets fit into the theory of biorthogonal multiwavelets. Quark vectors are used to define sequences of subspaces $ V_{p,j} $ of $ L_{2}(\mathbb{R}) $ which fulfill almost all conditions of a multiresolution analysis. Under some special conditions on the parameters they even satisfy all those properties. Moreover we prove that quarks and quarklets possess modulation matrices which fulfill the perfect reconstruction condition. Furthermore we show the existence of generalized dual quarks and quarklets which are known to be at least compactly supported tempered distributions from $\mathcal{S}'(\mathbb{R})$. Finally we also verify that quarks and quarklets can be used to define sequences of subspaces $ W_{p,j} $ of $ L_{2}(\mathbb{R}) $ that yield non-orthogonal decompositions of $ L_{2}(\mathbb{R}) $.
