A family of singular functions and its relation to harmonic fractal analysis and fuzzy logic
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De Gruyter Open
Singular functionHausdorff dimensionKatok foliationStrong negation
Amo, E.; Díaz Carrillo, M.; Fernández Sánchez, J. A family of singular functions and its relation to harmonic fractal analysis and fuzzy logic. Open Mathematics, 14: 1030-1052 (2016). [http://hdl.handle.net/10481/45164]
PatrocinadorThis work was supported by the Ministerio de Economía y Competitividad (Spain) under Research Project No. MTM2014-60594-P and partially supported by FEDER.
We study a parameterized family of singular functions which appears in a paper by H. Okamoto and M. Wunsch (2007). Various properties are revisited from the viewpoint of fractal geometry and probabilistic techniques. Hausdorff dimensions are calculated for several sets related to these functions, and new properties close to fractal analysis and strong negations are explored.