APPROXIMATION OF THE SAME BOX DIMENSION IN CONTINUOUS FUNCTIONS SPACE

Autor:	YONG-SHUN LIANG
Rok vydání:	2022
Předmět:	Applied Mathematics Modeling and Simulation Geometry and Topology
Zdroj:	Fractals. 30
ISSN:	1793-6543 0218-348X
DOI:	10.1142/s0218348x22500396
Popis:	In this paper, we make research on the approximation of functions with fractal dimension in continuous functions space. We first investigate fractal dimension of the linear combination of continuous functions with different fractal dimensions. Then, fractal winding of continuous functions has been given. Furthermore, based on Weierstrass theorem and Weierstrass function, we establish a theorem that continuous functions with the non-integer fractal dimension can be approximated by the linear combination of trigonometric polynomials with the same fractal dimension. Condition about continuous functions with fractal dimension one and two has also been discussed elementary.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4e5a0bc58f5629a410abe97cc492a539 https://doi.org/10.1142/s0218348x22500396 Zobrazit plný text záznamu