The Smoothness of Fractal Interpolation Functions on ℝ and on p-Series Local Fields
A fractal interpolation function on a p-series local field Kp is defined, and its p-type smoothness is shown by virtue of the equivalent relationship between the Hölder type space CσKp and the Lipschitz class Lipσ,Kp. The orders of the p-type derivatives and the fractal dimensions of the graphs of W...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/904576 |
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| Summary: | A fractal interpolation function on a p-series local field Kp is defined, and its p-type smoothness is shown by virtue of the equivalent relationship between the Hölder type space CσKp and the Lipschitz class Lipσ,Kp. The orders of the p-type derivatives and the fractal dimensions of the graphs of Weierstrass type function on local fields are given as an example. The α-fractal function on ℝ is introduced and the conclusion of its smoothness is improved in a more general case; some examples are shown to support the conclusion. Finally, a comparison between the fractal interpolation functions defined on ℝ and Kp is given. |
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| ISSN: | 1026-0226 1607-887X |