Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on generalized resolvents for ordinary differential operators


Author: Sung J. Lee
Journal: Proc. Amer. Math. Soc. 57 (1976), 279-282
MSC: Primary 34B25; Secondary 47E05
MathSciNet review: 0477252
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] E. A. Coddington, The spectral matrix and Green’s function for singular self-adjoint boundary value problems, Canadian J. Math. 6 (1954), 169–185. MR 0062905
  • [2] Earl A. Coddington, Generalized resolutions of the identity for symmetric ordinary differential operators, Ann. of Math. (2) 68 (1958), 378–392. MR 0103319
  • [3] Tosihusa Kimura and Mitiko Takahasi, Sur les opérateurs différentiels ordinaires linéaires formellement autoadjoints. I, Funkcial. Ekvac. 7 (1965), 35–90 (French). MR 0183923
  • [4] S. J. Lee, Ordinary differential operators with complex coefficients, Doctoral Dissertation, McMaster University, Hamilton, Ont., 1972.
  • [5] S. J. Lee, On boundary conditions for ordinary linear differential operators, J. London Math. Soc. (2) 12 (1975/76), no. 4, 447–454. MR 0412900
  • [6] -, Formally self-adjoint systems of differential equations, J. Math. Anal. Appl. (to appear).
  • [7] Sung J. Lee, Integrability of certain solutions of differential equations, Period. Math. Hungar. 7 (1976), no. 3-4, 233–237. MR 0454142
  • [8] M. A. Naĭmark, Linear differential operators, GITTL, Moscow, 1954; English transl., Part II, Ungar, New York, 1968. MR 16, 702; 41 #7485.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34B25, 47E05

Retrieve articles in all journals with MSC: 34B25, 47E05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0477252-1
Keywords: Symmetric differential operator, generalized resolvent, fundamental solutions
Article copyright: © Copyright 1976 American Mathematical Society