On the Completeness of Root Functions of Pencils of Linear Ordinary Differential Operators with General Boundary Conditions

(C, 1)-Summability of Fourier Series in Root Functions of Ordinary Linear Differential Operators in a Space of Vector Functions

“…Tamarkin [1] generalized these results to Fourier series in root functions of ordinary differential pencils. The restrictive conditions imposed in [1] were eliminated in [2]. In the authors' opinion, it is of interest to consider a similar problem for arbitrary basis systems occurring in Il'in's work (e.g., see [3]) on ordinary differential operators.…”

“…BASIC NOTIONS AND CONSTRUCTIONS RELATED TO THE OPERATOR (1), (2) 1. Throughout the following, we assume that the operator (1), (2) satisfies the following conditions.…”

“…For each componentwise bounded integrable vector function h(x) on [a, b], the series (20) [that is, the Fourier series in eigenelements of the regular operator (1), (2)] is (C, 1)-summable almost everywhere on (a, b) to h(x). In other words, one has…”