Cauchy dual Subnormality of extensions of $m$-isometric composition operators on directed graphs

Abstract

In this paper, we discuss the analyticity, ${\Delta }_{C_{\varphi }}$- regularity, kernel condition and subnormality of Cauchy dual of $k$-quasi-$m$-isometric composition operators on directed graphs with one circuit and multiple branching vertices.

Preliminary Draft, 13 pages