کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8904905 | 1633760 | 2018 | 39 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Differentiability and Hölder spectra of a class of self-affine functions
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Differentiability and Hölder spectra of a class of self-affine functions Differentiability and Hölder spectra of a class of self-affine functions](/preview/png/8904905.png)
چکیده انگلیسی
This paper studies a large class of continuous functions f:[0,1]âRd whose range is the attractor of an iterated function system {S1,â¦,Sm} consisting of similitudes. This class includes such classical examples as Pólya's space-filling curves, the Riesz-Nagy singular functions and Okamoto's functions. The differentiability of f is completely classified in terms of the contraction ratios of the maps S1,â¦,Sm. Generalizing results of Lax (1973) and Okamoto (2006), it is shown that either (i) f is nowhere differentiable; (ii) f is non-differentiable almost everywhere but with uncountably many exceptions; or (iii) f is differentiable almost everywhere but with uncountably many exceptions. The Hausdorff dimension of the exceptional sets in cases (ii) and (iii) above is calculated, and more generally, the complete multifractal spectrum of f is determined.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 328, 13 April 2018, Pages 1-39
Journal: Advances in Mathematics - Volume 328, 13 April 2018, Pages 1-39
نویسندگان
Pieter C. Allaart,