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Matematicheskie Zametki, 2007, Volume 81, Issue 6, Pages 924–938
DOI: https://doi.org/10.4213/mzm3741 (Mi mzm3741) 		 
This article is cited in 29 scientific papers (total in 29 papers)

On the Construction and Some Properties of Self-Similar Functions in the Spaces $L_p[0,1]$

I. A. Sheipak

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (560 kB) Citations (29)
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DOI: https://doi.org/10.4213/mzm3741
Abstract: We present a construction of affinely self-similar functions. In terms of the parameters of self-similarity transformations, a condition is given for these functions to belong to the classes $L_p[0,1]$ as well as to the space $C[0,1]$. Some properties of these functions (monotonicity and bounded variation) are studied. A relationship between self-similar functions and self-similar measures is established.
Keywords: self-similar function, self-similar measure, fractal curve, monotonicity, function of bounded variation, Lebesgue classes.
Received: 28.06.2006
Revised: 29.09.2006
English version:
Mathematical Notes, 2007, Volume 81, Issue 6, Pages 827–839
DOI: https://doi.org/10.1134/S0001434607050306
Bibliographic databases:
UDC: 517.518
Language: Russian
Citation: I. A. Sheipak, “On the Construction and Some Properties of Self-Similar Functions in the Spaces $L_p[0,1]$”, Mat. Zametki, 81:6 (2007), 924–938; Math. Notes, 81:6 (2007), 827–839
Citation in format AMSBIB
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    • This publication is cited in the following 29 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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