A family of singular functions and its relation to harmonic fractal analysis and fuzzy logic
Metadatos
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De Gruyter Open
Materia
Singular function Hausdorff dimension Katok foliation Strong negation
Date
2016Referencia bibliográfica
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]
Patrocinador
This work was supported by the Ministerio de Economía y Competitividad (Spain) under Research Project No. MTM2014-60594-P and partially supported by FEDER.Résumé
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.