On the construction and some properties of self-similar functions in the spaces L p[0, 1] |
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Authors: | I. A. Sheipak |
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Affiliation: | 1. Lomonosov Moscow State University, Russia
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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. |
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