Multifractal formalism and anisotropic selfsimilar functions

被引：33

作者：

Ben Slimane, M ^{[1
]}

机构：

[1] Fac Sci Tunis, Dept Math, Tunis 1060, Tunisia

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 1998年 / 124卷

关键词：

D O I：

10.1017/S0305004198002710

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove that the conjectures of Frisch and Parisi and Arneodo et al. (called the multifractal formalism for functions) may fail for some non-homogeneous selfsimilar functions on R-2. In these cases, we compute the correct spectrum of singularities and we show how the multifractal formalism must be modified.

引用

页码：329 / 363

页数：35

共 21 条

[1] Adams R, 1978, Sobolev spaces
[2] SINGULARITY SPECTRUM OF FRACTAL SIGNALS FROM WAVELET ANALYSIS - EXACT RESULTS
BACRY, E
MUZY, JF
ARNEODO, A
[J]. JOURNAL OF STATISTICAL PHYSICS, 1993, 70 (3-4) : 635 - 674
[3] BenSlimane M, 1997, CR ACAD SCI I-MATH, V324, P981
[4] BENSLIMANE M, IN PRESS CONSTR APPR
[5] ATOMIC DECOMPOSITION OF DISTRIBUTIONS IN PARABOLIC HP SPACES
CALDERON, AP
[J]. ADVANCES IN MATHEMATICS, 1977, 25 (03) : 216 - 225
[6] PARABOLIC MAXIMAL FUNCTIONS ASSOCIATED WITH A DISTRIBUTION .2.
CALDERON, AP
TORCHINSKY, A
[J]. ADVANCES IN MATHEMATICS, 1977, 24 (02) : 101 - 171
[7] ON THE THERMODYNAMIC FORMALISM FOR MULTIFRACTAL FUNCTIONS
DAUBECHIES, I
LAGARIAS, JC
[J]. REVIEWS IN MATHEMATICAL PHYSICS, 1994, 6 (5A) : 1033 - 1070
[8] Falconer K., 1990, FRACTAL GEOMETRY MAT, V2
[9] FOLLAND GB, 1993, MATH NOTES, V28
[10] FRISCH U, 1985, P INT SUMM SCH PHYS, P84

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