Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fractal operator associated to bivariate fractal interpolation
  functions   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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The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
18
The categories of this paper are: econ