Basis Properties of Eigenfunctions of Second‐Order Differential Operators with Involution

Abstract

We study the basis properties of systems of eigenfunctions and associated functions for one kind of generalized spectral problems for a second-order ordinary differential operator.

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

“…In this paper, we shall use a spectral problem for ordinary differential operators with involution. Such and similar spectral problems are considered in previous studies …”

“…Such and similar spectral problems are considered in previous studies. [36][37][38][39][40][41][42][43][44][45][46][47] Definition. By a regular solution of the inverse problem (5) to (8), we mean a pair of functions (u(x, t), (x)) of the class u(x, t) ∈ C 2,1…”

Inverse problems for a nonlocal wave equation with an involution perturbation

“…By expressing the function X as a sum of even and odd functions [13], it can be shown that the problem (3.1), (3.2) has the following eigenvalues…”

“…Also, differential equations with operations on the space variable received great attention starting with Carleman [6] (equations with shift (involution)) and followed with great attention by Przewoerska-Rolewicz [17,18,19,20,21,22,23], Aftabizadeh et al [1], Andreev [3], [4], Burlutskayaa et al [5], Gupta [7], [8], [9], Watkins [31], Viner [29], [30], and Wiener [32], [33]; for spectral problems and inverse problems for equations with involutions we may cite the recent works of Kaliev et al [10], [11], Sadybekov et al [15], [16], [25], Sarsenbi et al [13], [26] and [27]. The papers of Aliev [2] and Rus [24] concern the maximum principle for equations with a delay in the space variable.…”

On Spectral Properties of a Boundary Value Problem of the First Order Equation With Deviating Argument

“…These studies were continued in the cycle of works by M.A. Sadybekov and A.M. Sarsenby [30][31][32][33][34][35]. Over the past decade, interest of researchers to differential equations with involutions has noticeably increased, as evidenced by the publications [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52].…”