Fractal Frames of Functions on the Rectangle

Fractal and Fractional

MaríaA. Navascués¹  Md.Nasim Akhtar²  Ram Mohapatra³ 

[1] Departamento de Matemática Aplicada, Universidad de Zaragoza, 50018 Zaragoza, Spain;Department of Mathematics, Presidency University, 86/1, College Street, Kolkata 700 073, India;Department of Mathematics, University of Central Florida, Orlando, FL 32817, USA;

关键词: fractals;    Iterated function systems;    fractal interpolation functions;    function spaces;   

DOI  :  10.3390/fractalfract5020042

来源: DOAJ

【 摘 要 】

In this paper, we define fractal bases and fractal frames of ${\mathcal{L}}^2(I\times J)$, where I and J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of ${\mathcal{L}}^2(I\times J)$ with the tensor product space ${\mathcal{L}}^2\left(I\right)⨂{\mathcal{L}}^2\left(J\right)$. First, we recall the procedure of constructing a fractal perturbation of a continuous or integrable function. Then, we define fractal frames and bases of ${\mathcal{L}}^2(I\times J)$ composed of product of such fractal functions. We also obtain weaker families as Bessel, Riesz and Schauder sequences for the same space. Additionally, we study some properties of the tensor product of the fractal operators associated with the maps corresponding to each variable.

【 授权许可】

Unknown