Left‐definite problems of regular self‐adjoint differential equations of even order

Abstract

Key words Left-definiteness, left-definite space, boundary condition MSC (2010) Primary: 34B05, Secondary: 34L05, 47E05The left-definite boundary conditions of the problem consisting of a regular formally self-adjoint differential equation of even order and a self-adjoint boundary condition are characterized in terms of a certain fundamental set of solutions of the equation. Based on the left-definite boundary conditions, all the left-definite spaces of the problem are described explicitly.