Convergence and Approximation of the Sturm–Liouville Operators with Potentials-Distributions

• Date: 2015
• Main Authors: Goryunov, A. S., Горюнов, А. С.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2008
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study the operators $L_n y = −(p_n y′)′+q_n y, n ∈ ℤ_{+}$, given on a finite interval with various boundary conditions. It is assumed that the function $q_n$ is a derivative (in a sense of distributions) of $Q_n$ and $1/p_n , Q_n /p_n$, and $Q^2_n/p_n $ are integrable complex-valued functions. Th...