Properties of locally linearly independent refinable function vectors
نویسندگان
چکیده
منابع مشابه
Properties of locally linearly independent refinable function vectors
where j is in KÁo (A) if Áo(¢ ¡ j) 6 ́ 0 on A. The function vector © is said to be globally linearly independent if in the above de ̄nition A = IR. Hence, local linear independence of © implies global linear independence. For re ̄nable functions (r = 1) with dilation parameter 2 local and global linear independence are equivalent. However, for r > 1 this is not longer true. The description of loca...
متن کاملSupports of Locally Linearly Independent M-Refinable Functions, Attractors of Iterated Function Systems and Tilings
We study supports of M -re ̄nable functions by means of attractors of iterated function systems, where M is an integer greater than (or equal to) 2. Most of the time, the re ̄nable function Á is not explicitly known. We need to study their properties from the re ̄nement mask. Under the assumption of local linear independence, we show that the support equals to the attractor of an iterated function...
متن کاملHow Many Holes Can Locally Linearly Independent Reenable Function Vectors Have?
In this paper we consider the support properties of locally linearly independent re nable function vectors r T We propose an algorithm for computing the global support of the components of Further for T we investigate the supports especially the possibility of holes of re nable function vectors if local linear independence is assumed Finally we give some necessary conditions for local linear in...
متن کاملGeneralized interpolating refinable function vectors
Interpolating scalar refinable functions with compact support are of interest in several applications such as sampling theory, signal processing, computer graphics, and numerical algorithms. In this paper, we shall generalize the notion of interpolating scalar refinable functions to compactly supported interpolating d-refinable function vectors with any multiplicity r and dilation factor d. Mor...
متن کاملMultiwavelet Frames from Refinable Function Vectors
Starting from any two compactly supported d-refinable function vectors in ( L2(R) )r with multiplicity r and dilation factor d, we show that it is always possible to construct 2rd wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2(R) and they achieve the best possible orders of vanishing moments. When all the components of the two real-valued d-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2003
ISSN: 0021-9045
DOI: 10.1016/s0021-9045(03)00036-4