Regularity of Butterworth refinable functions
نویسندگان
چکیده
منابع مشابه
Sobolev exponents of Butterworth refinable functions
The precise Sobolev exponent s∞(φn) of the Butterworth refinable function φn associated with the Butterworth filter of order n, bn(ξ) := cos2n(ξ/2) cos2n(ξ/2)+sin2n(ξ/2) , is shown to be s∞(φn) = n log2 3+ log2(1+ 3−n). This recovers the previously given asymptotic estimate of s∞(φn) of Fan and Sun [1], and gives more accurate regularity of Butterworth refinable function φn. AMS 2000 Subject Cl...
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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):
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ژورنال
عنوان ژورنال: Asian Journal of Mathematics
سال: 2001
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.2001.v5.n3.a2