Theory of sectorial operators and its application in Fractional calculus (Chapter 5)

Maksim V. Kukushkin

Published 2024-01-11Version 1

In this chapter, we formulated the sufficient conditions of the Abel-Lidskii basis property for a sectorial non-selfadjoint operator of the special type. Having studied such an operator class, we strengthened the conditions regarding the semi-angle of the sector and weakened a great deal conditions regarding the involved parameters. Thus, we clarified the results by Lidskii devoted to the decomposition on the root vector system of the non-selfadjoint operator. We used a technique of the entire function theory and introduced the so-called Schatten-von Neumann class of the convergence exponent. Having considered strictly accretive operators satisfying special conditions formulated in terms of the norm and used a sequence of contours of the power type, we invented a peculiar method how to calculate a contour integral involved in the problem.