Basis Properties in Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{L}}_{{\varvec{p}}}$$\end{document} of Root Functions of Sturm–Liouville Problem with Spectral Parameter-Dependent Boundary Conditions

In this paper, we consider the Sturm–Liouville problem with spectral parameter in the boundary conditions. We associate this problem with a self-adjoint operator in the Pontryagin space Π2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi _{2}$$\end{document}. Using this operator-theoretic formulation and analytic methods, we study the basis properties in the space Lp(0,1),1<p<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{p} (0,1),\,1<p < \infty $$\end{document}, of systems of root functions of this problem.