Fractal Convolution Bessel Sequences on Rectangle

Fractal functions provide a natural deterministic approximation of complex phenomena and also it has self-similarity. Recently, it has been recognized as an internal binary operation, called fractal convolution. In the present article, we obtain Bessel sequences of $$L^2(\mathcal {I} \times \mathcal {J})$$ composed of product of fractal convolutions, using the identification of $$L^2(\mathcal {I} \times \mathcal {J})$$ with the tensor product space $$L^2(\mathcal {I})\otimes L^2(\mathcal {J})$$ , where $$\mathcal {I}$$ and $$\mathcal {J}$$ are real compact intervals.