Spectral Analysis for Linear Pencils N — λP of Ordinary Differential Operators

Boundary eigenvalue problems for linear pencils N — λ of two ordinary differential operators are studied where P is of lower order than N. In a suitable scale of subspaces of Sobolev spaces and spaces of continuously differentiable functions results on minimality and basis properties of the eigenfunctions and associated functions are proved, including explicit formulas for the Fourier coefficients. As an application the Orr - Sommerfeld equation is considered.