On the invariance principle for a characteristic function

TL;DR

This paper extends the invariance principle for characteristic functions associated with dissipative operators to include all transformations in the special linear group SL_2(R), broadening the scope of symmetry considerations.

Contribution

It generalizes the invariance principle from affine transformations to the entire group SL_2(R), providing a more comprehensive understanding of the symmetry properties of characteristic functions.

Findings

Extended invariance principle to SL_2(R) transformations.

Broadened the class of symmetries for dissipative operators.

Enhanced theoretical framework for characteristic functions.

Abstract

We extend the invariance principle for a characteristic function of a dissipative operator with respect to the group of affine transformations of the real axis preserving the orientation to the case of general $SL_2(\bbR)$ transformations.