Fractal Frames of Functions on the Rectangle

In this paper, we define fractal bases and frames of L2(I×J), where I J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification L2(I×J) with tensor product space L2(I)⨂L2(J). First, recall procedure constructing perturbation continuous or integrable function. Then, composed such functions. We also obtain weaker families as Bessel, Riesz Schauder sequences for same space. Additionally, study some properties operators associated corresponding each variable.