Natural lacunae method and Schatten-von Neumann classes of the convergence exponent

TL;DR

This paper introduces a new approach using entire function theory and Schatten-von Neumann classes to analyze the spectral decomposition of non-selfadjoint operators, extending Lidskii's results with novel contour constructions.

Contribution

It develops a new method employing Schatten-von Neumann classes and contour techniques of power type for spectral analysis of accretive operators, improving upon previous exponential type contours.

Findings

Established a new class of convergence exponents.

Constructed power-type contours for spectral decomposition.

Extended Lidskii's results to broader operator classes.

Abstract

The first our aim is to clarify the results obtained by Lidskii devoted to the decomposition on the root vector system of the non-selfadjoint operator. We use a technique of the entire function theory and introduce a so-called Schatten-von Neumann class of the convergence exponent. Considering strictly accretive operators satisfying special conditions formulated in terms of the norm, we construct a sequence of contours of the power type on the contrary to the results by Lidskii, where a sequence of contours of the exponential type was used.