Polynomial functions are re nable
نویسنده
چکیده
Received (Day Month Year) Revised (Day Month Year) Communicated by (xxxxxxxxxx) The scope of renable 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 renable. This may yield an interesting notion of convolution of polynomials.
منابع مشابه
Stability and Independence of the Shifts of Finitely Many Refinable Functions
Typical constructions of wavelets depend on the stability of the shifts of an underlying re nable function. Unfortunately, several desirable properties are not available with compactly supported orthogonal wavelets, e.g. symmetry and piecewise polynomial structure. Presently, multiwavelets seem to o er a satisfactory alternative. The study of multiwavelets involves the consideration of the prop...
متن کاملConvergence and Boundedness of Cascade Algorithm in Besov Spaces and Triebel-lizorkin Spaces Running Title Convergence and Boundedness of Cascade Algorithm
In this paper, by introducing characteristic polynomial of a cascade algorithm and joint spectral radius on a nitely dimensional space, we give complete characterization of the rate of convergence and increment of the cascade algorithm in Besov spaces and TriebelLizorkin spaces. Also moment conditions of the initial distribution and the re nable distribution in the cascade algorithm, close rela...
متن کاملA Construction of Bi orthogonal Functions to B splines with Multiple Knots
We present a construction of a re nable compactly supported vector of functions which is bi orthogonal to the vector of B splines of a given degree with multiple knots at the integers with prescribed multiplicity The construction is based on Hermite interpolatory subdivision schemes and on the relation between B splines and divided di erences The bi orthogonal vector of functions is shown to be...
متن کاملSome Notes on Two Scale Di erence Equations
In this paper we continue our considerations in on two scale di erence equations mainly with respect to continuous solutions Moreover we study re nable step functions and piecewise polynomials Also solutions with noncompact support are considered New algorithms for the approximative computation of continuous solutions are derived
متن کاملApproximation Properties of Multi Scaling Functions A Fourier Approach
In this paper we consider approximation properties of a nite set of functions r which are not necessarily compactly supported but have a suitable decay rate Assuming that the function vector r is re n able we sketch a new way how to derive necessary and su cient conditions for the re nement mask in Fourier domain Introduction For applications of multi wavelets in nite element methods the proble...
متن کامل