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Spectral Theory Of Self-Adjoint Ordinary Differential Operators, Charles C. Oehring

Doctoral Dissertations

Introduction: Many of the properties of the ordinary Fourier series expansion of a given function are shared by the orthogonal expansion in terms of eigenfunctions of a second order ordinary differential operator. Let p = p(x) and q = q(x) be real-valued functions such that p, p', and q are continuous, and p(x) > 0, on a finite interval a ≤ x ≤ b. Let λ be a complex parameter. The classical Strum-Liouville theory [9, section 27; 4, Chapter 7; 21, Chapter 1]¹ is concerned with solutions of the differential equation -(py') + qy = λ, which satisfy certain real …