Vishal Agrawal and Tanmoy Som
Some Properties of Fractal Operator Associated with Complex-Valued Fractal Functions on the Sierpinski Gasket
Dynamic Systems and Applications 32 (2023) 369-382

https://doi.org/10.46719/dsa2023.32.20

ABSTRACT.
In this paper, we demonstrate several properties, such as Fredholm, non-compactness of the complex-valued fractal operator associated with the complex-valued fractal functions, which is constructed using a germ function, base function, and scaling functions defined on the Sierpinski gasket. We show the existence of a non-trivial closed subspace of a complex-valued fractal operator. We prove that a complex-valued fractal function has finite energy under certain conditions on the parameters involved. Further, the existence of Schauder basis consisting of a complex-valued fractal function is shown.

AMS (MOS) Subject Classification. Primary 28A80, Secondary 10K50, 41A10.

Key Words and Phrases. Complex-valued fractal function; Sierpinski gasket, Schauder basis, Energy, Fractal operator.