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arXiv · 1810.09701

A fractal operator associated to bivariate fractal interpolation functions

S. Verma·P. Viswanathan
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Abstract

A general framework to construct fractal interpolation surfaces (FISs) on rectangular grids was presented and bilinear FIS was deduced by Ruan and Xu [Bull. Aust. Math. Soc. 91(3), 2015, pp. 435-446]. From the view point of operator theory and the stand point of developing some approximation aspects, we revisit the aforementioned construction to obtain a fractal analogue of a prescribed continuous function defined on a rectangular region in $R^2$. This approach leads to a bounded linear operator analogous to the so-called $\alpha$-fractal operator associated with the univariate fractal interpolation function. Several elementary properties of this bivariate fractal operator are reported. We extend the fractal operator to the Lp-spaces for $1 \le p < \infty$. Some approximation aspects of the bivariate continuous fractal functions are also discussed.

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S. Verma, P. Viswanathan. 2018-10-23. A fractal operator associated to bivariate fractal interpolation functions. https://arxiv.org/abs/1810.09701

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