Division problem of the perturbed form of order one of the Chebyshev form of second kind

Abstract

We study the regularity of the form ( linear functional) satisfying
the functional equation $(x^2-c^2)u=\lambda v$ where
$c\in\mathbb{C},\lambda\in \mathbb{C}-\{0\}$ and $v$ is the
perturbed form of order one of the Chebyshev form of second kind.
The integral representation of the form $ u $ is highlighted.
Moreover, some symmetric second degree forms of class
two and four are given.