Accuracy of Lattice Translates of Several Multidimensional Refinable Functions
نویسندگان
چکیده
منابع مشابه
Accuracy of Lattice Translates of Several Multidimensional Reenable Functions
Complex-valued functions f 1 ; : : : ; f r on R d are reenable if they are linear combinations of nitely many of the rescaled and translated functions f i (Ax?k), where the translates k are taken along a lattice ? R d and A is a dilation matrix that expansively maps ? into itself. Reenable functions satisfy a reenement equation f(x) = P k2 c k f(Ax ? k), where is a nite subset of ?, the c k are...
متن کاملSmoothness of Multiple Refinable Functions
We consider the smoothness of solutions of a system of refinement equations written in the form φ = ∑ α∈Z a(α)φ(2 · − α), where the vector of functions φ = (φ1, . . . , φr) is in (Lp(R)) and a is a finitely supported sequence of r× r matrices called the refinement mask. We use the generalized Lipschitz space Lip∗(ν, Lp(R)), ν > 0, to measure smoothness of a given function. Our method is to rela...
متن کاملThe Limits of Refinable Functions
A function φ is refinable (φ ∈ S) if it is in the closed span of {φ(2x−k)}. This set S is not closed in L2(R), and we characterize its closure. A necessary and sufficient condition for a function to be refinable is presented without any information on the refinement mask. The Fourier transform of every f ∈ S \ S vanishes on a set of positive measure. As an example, we show that all functions wi...
متن کاملAffine Similarity of Refinable Functions
In this paper, we consider certain affine similarity of refinable functions and establish certain connection between some local and global properties of refinable functions, such as local and global linear independence , local smoothness and B-spline, local and global Hölder continuity.
متن کاملPolynomial functions are refinable
The scope of refinable functions in wavelet theory is focused to localized functions. In our paper we like to widen that scope, in particular we show that all polynomial functions are refinable. This may yield an interesting notion of convolution of polynomials.
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: 1998
ISSN: 0021-9045
DOI: 10.1006/jath.1997.3211