VII.—On the Spectrum of Ordinary Second Order Differential Operators.
- 1 January 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences
- Vol. 68 (2) , 95-119
- https://doi.org/10.1017/s0080454100008293
Abstract
This paper considers properties of the spectrum of differential operators derived from differential expressions of the second order. The object is to link the spectral properties of these differential operators with the analytic, function-theoretic properties of the solutions of the differential equation. This provides an alternative approach to the spectral theory of these differential operators but one which is consistent with the standard definitions used in Hilbert space theory. In this way the approach may be of interest to applied mathematicians and theoretical physicists.Keywords
This publication has 4 references indexed in Scilit:
- A NOTE ON THE SELF-ADJOINT DOMAINS OF SECOND-ORDER DIFFERENTIAL EQUATIONSThe Quarterly Journal of Mathematics, 1963
- Eigenfunction Expansions Associated with Second-order Differential Equations, Part 1Physics Today, 1962
- On the Nature of the Spectrum of Singular Second Order Linear Differential EquationsCanadian Journal of Mathematics, 1951
- The Eigenvalue Problem for Ordinary Differential Equations of the Second Order and Heisenberg's Theory of S-MatricesAmerican Journal of Mathematics, 1949