The Glazman-Krein-Naimark Theorem for Ordinary Differential Operators
The original form of symmetric boundary conditions for Lagrange symmetric (formally self-adjoint) ordinary linear differential expressions, was obtained by I.M. Glazman in his seminal paper of 1950. This result described all self-adjoint differential operators, in the underlying Hilbert function space, generated by real even-order differential expressions.
KeywordsLinear Manifold Linear Differential Operator Chapter Versus Ordinary Differential Operator Deficiency Index
Unable to display preview. Download preview PDF.
- N.I. Akhiezer and I.M. Glazman. Theory of linear operators in Hilbert space; I and II. (Pitman and Scottish Academic Press, London and Edinburgh; 1980: translated, from the material prepared for the third Russian edition of 1978, by E.R. Dawson and edited by W.N. Everitt.)Google Scholar
- N. Dunford and J.T. Schwartz. Linear operators II: Spectral theory. (Wiley, New York; 1963.)Google Scholar
- W.N. Everitt. ‘On the deficiency index problem for ordinary differential operators.’ Lecture notes for the 1977 International Conference: Differential Equations, Uppsala, Sweden; pages 62 to 81. (University of Uppsala, Sweden, 1977; distributed by Almquist and Wiskell International, Stockholm, Sweden.)Google Scholar
- W.N. Everitt. ‘Linear ordinary quasi-differential expressions’. Lecture notes for the Fourth International Symposium on Differential Equations and Differential Geometry, Beijing, Peoples’ Republic of China 1983; pages 1 to 28. (Department of Mathematics, University of Beijing, Peoples’ Republic of China; 1986.)Google Scholar
- W.N. Everitt and L. Markus. Boundary value problems and symplectic geometry for ordinary differential and quasi-differential equations. (In manuscript; to be submitted for publication in 1996.)Google Scholar
- M.A. Naimark. Linear differential operators; II. (Ungar, New York; 1968: translated from the second Russian edition of 1966 by E.R. Dawson, and edited by W.N. Everitt.)Google Scholar
- D. Shin. ‘Existence theorems for quasi-differential equations of order n.’ Doklad. Akad. Nauk SSSR. 18 (1938), 515–518.Google Scholar
- D. Shin. ‘On quasi-differential operators in Hilbert space.’ Doklad. Akad. Nauk. SSSR. 18 (1938), 523–526.Google Scholar
- D. Shin. ‘On the solutions of a linear quasi-differential equation of order n.’ Mat. Sb. 7 (1940), 479–532.Google Scholar
- J. Weidmann. Spectral theory of ordinary differential operators. (Lecture Notes in Mathematics, 1259; Springer-Verlag, Berlin and Heidelberg; 1987.)Google Scholar