基于合并隐变量FIF的多分辨分析
Multiresolution Analysis Based on Coalescence Hidden-variable FIF
摘要：
本文对聚并隐变量分形插值函数进行了多分辨分析。在基于CHFIF的多分辨率分析中，具有CHFIF的更大的自由变元和约束变量集合的可用性在L2（\mathbb{R}）中的函数重构中提供了比仅基于仿射分形插值函数（AFIF）的多分辨率分析所提供的更多的控制。在我们的方法中，引入了CHFIFs的向量空间，确定了它的维数，构造了L2（\mathbb{R}）\cap C 0（\mathbb{R}）中某些CHFIFs组成的向量子空间Vk，k \in \mathbb{Z}的Riesz基.作为一种特殊情况，对于4维CHFIFs的向量空间，向量子空间Vk，k \in \mathbb{Z}的正交基被明确地构造，并且使用这些基，生成紧支撑的连续正交小波。
英文摘要：
In the present paper, multiresolution analysis arising from Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is accomplished. The availability of a larger set of free variables and constrained variables with CHFIF in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in L2(\mathbb{R})than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs). In our approach, the vector space of CHFIFs is introduced, its dimension is determined and Riesz bases of vector subspaces Vk, k \in \mathbb{Z}, consisting of certain CHFIFs in L2(\mathbb{R}) \cap C0(\mathbb{R}) are constructed. As a special case, for the vector space of CHFIFs of dimension 4, orthogonal bases for the vector subspaces Vk, k \in \mathbb{Z}, are explicitly constructed and, using these bases, compactly supported continuous orthonormal wavelets are generated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
