Singular perturbations of fractionally-differential operators on the circle

Abstract

In the article we study strongly singular perturbations, in general non-symmetric, of the non-negative fractionally-differential operators $\mathbb{D}^{2s}$ of order $s\in (1/2,\infty)$ on the circle, which coincides up to multiplier with derivative of H. Weyl. We define the perturbed operators, investigate their common spectral properties.