A note on generalized resolvents for ordinary differential operators
HTML articles powered by AMS MathViewer
- by Sung J. Lee PDF
- Proc. Amer. Math. Soc. 57 (1976), 279-282 Request permission
Abstract:
We give an explicit construction for the kernel of an arbitrary generalized resolvent for an ordinary symmetric differential operator. In particular, this avoids the use of approximation of selfadjoint operators on compact intervals. We also discuss integrability of functions which are adjoint to certain fundamental solutions.References
- E. A. Coddington, The spectral matrix and Green’s function for singular self-adjoint boundary value problems, Canad. J. Math. 6 (1954), 169–185. MR 62905, DOI 10.4153/cjm-1954-019-4
- Earl A. Coddington, Generalized resolutions of the identity for symmetric ordinary differential operators, Ann. of Math. (2) 68 (1958), 378–392. MR 103319, DOI 10.2307/1970253
- Tosihusa Kimura and Mitiko Takahasi, Sur les opérateurs différentiels ordinaires linéaires formellement autoadjoints. I, Funkcial. Ekvac. 7 (1965), 35–90 (French). MR 183923 S. J. Lee, Ordinary differential operators with complex coefficients, Doctoral Dissertation, McMaster University, Hamilton, Ont., 1972.
- S. J. Lee, On boundary conditions for ordinary linear differential operators, J. London Math. Soc. (2) 12 (1975/76), no. 4, 447–454. MR 412900, DOI 10.1112/jlms/s2-12.4.447 —, Formally self-adjoint systems of differential equations, J. Math. Anal. Appl. (to appear).
- Sung J. Lee, Integrability of certain solutions of differential equations, Period. Math. Hungar. 7 (1976), no. 3-4, 233–237. MR 454142, DOI 10.1007/BF02017941 M. A. Naĭmark, Linear differential operators, GITTL, Moscow, 1954; English transl., Part II, Ungar, New York, 1968. MR 16, 702; 41 #7485.
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 279-282
- MSC: Primary 34B25; Secondary 47E05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0477252-1
- MathSciNet review: 0477252