Regularity of Multivariate Re nable Functions
نویسندگان
چکیده
The regularity of a univariate compactly supported reenable function is known to be related to the spectral properties of an associated transfer operator. In the case of multivariate reenable functions with a general dilation matrix A, although factorization techniques, which are typically used in the univariate setting, are no longer applicable, we derive similar results that also depend on the spectral properties of A.
منابع مشابه
Multivariate Compactly Supported Fundamental Re nable Functions
For a given continuous compactly supported reenable function that is fundamental (that means, () =), this paper presents several methods to construct, directly from , compactly supported fundamental reenable functions with higher regularity. Asymptotic regularity analyses of the constructions are given. These constructions immediately provide multivariate interpolatory subdivision schemes that ...
متن کاملFundamental Re nable Functions , Duals and Biorthogonal
In areas of geometric modeling and wavelets, one often needs to construct a compactly supported reenable function with suucient regularity which is fundamental for interpolation (that means, (0) = 1 and () = 0 for all 2 Z s nf0g). Low regularity examples of such functions have been obtained numerically by several authors and a more general numerical scheme was given in RiS1]. This paper present...
متن کاملRegularity of Butterworth Re nable Functions
Ai Hua FAN and Qiyu SUN Abstract Let N be the re nable function with Butterworth lter cos2N 2( cos2N 2 +sin2N 2) 1, and let sp( N) be the Sobolev exponent of N of order p (0 < p 1). It is proved in this note that there exists a constant 0 < r = rp < 1 such that ln(1 + rN) ln 2 sp( N) N ln 3 ln 2 ln(1 + 3 N) ln 2 ; (8N 1):
متن کاملStability and Independence for Multivariate Re nable Distributions
Due to their so-called time-frequency localization properties, wavelets have become a powerful tool in signal analysis and image processing. Typical constructions of wavelets depend on the stability of the shifts of an underlying re nable function. In this paper, we derive necessary and su cient conditions for the stability of the shifts of certain compactly supported re nable functions. These ...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998