×

Duality theory for N-th order differential operators under Stieltjes boundary conditions. II: Nonsmooth coefficients and nonsingular measures. (English) Zbl 0316.47027


MSC:

47E05 General theory of ordinary differential operators
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Arghiriade, E., Sur l’inverse généralisée d’un opérateur linéaire dans les espaces de Hilbert, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 45, 8, 471-477 (1968) · Zbl 0186.45103
[2] Arens, R., Operational calculus of linear relations, Pacific J. Math., 11, 9-23 (1961) · Zbl 0102.10201
[3] Ben-Israel, A.; Greville, T. N. E., Generalised Inverses: Theory and Applications (1974), New York: Interscience, New York · Zbl 0305.15001
[4] R. C. Brown,The adjoint and Fredholm index of a linear system with general boundary conditions, Univ. of Wisconsin-Madison, Mathematics Research Center TSR no. 1287.
[5] Brown, R. C., Generalised Green’s functions and generalised inverses for linear differential systems with Stieltjes boundary conditions, J. Differential Equations, 16, 335-351 (1974) · Zbl 0291.34043
[6] R. C. Brown,Duality theory for n-thorder differential operators under Stieltjes boundary conditions, University of Wisconsin-Madison, Mathematics Research Center TSR no. 1329 (1973).
[7] Brown, R. C., Adjoint domains and generalized splines, Czech. Math. J., 25, 100, 134-147 (1975) · Zbl 0309.41014
[8] Brown, R. C.; Krall, A. M., Ordinary differential operators under Stieltjes boundary conditions, Trans. Amer. Math. Soc., 198, 73-91 (1974) · Zbl 0295.34010
[9] Chitwood, H., Generalized Green’s matrices for linear differential systems, SIAM J. Math. Anal., 4, 104-109 (1973) · Zbl 0252.34019
[10] H. Chitwood,Generalized Green’s matrices for linear differential system, University of Tennessee Ph. D. dissertation (1971). · Zbl 0226.34009
[11] Dunford, N.; Schwartz, J., Linear Operators, Part I (1957), New York: Interscience, New York
[12] Goldberg, S., Unbounded Linear Operators (1966), New York: McGraw-Hill, New York
[13] Locker, J., Self-adjointness for multi-point differential operators, Pacific J. Math., 45, 561-570 (1973) · Zbl 0254.47058
[14] Naimark, M. A., Linear Differential Operators, Part I (1968), New York: Ungar, New York · Zbl 0227.34020
[15] Naimark, M. A., Linear Differential Operators, Part II (1968), New York: Ungar, New York · Zbl 0227.34020
[16] Nashed, M. Z.; Rall, L. B., Generalized Inverses, Normal Solvability and Iteration for Singular Operator Equations, Nonlinear Functional Analysis, 311-359 (1971), New York: Academic Press, New York
[17] Reid, W. T., Generalized Green’s matrices for compatible systems of differential equations, Amer. J. Math., 53, 443-459 (1931) · JFM 57.0525.01
[18] Reid, W. T., Generalized Green’s matrices for two-point boundary problems, SIAM J. Appl. Math., 15, 856-870 (1967) · Zbl 0157.15304
[19] W. T. Reid,Generalized inverses of differential and integral operators, «Theory and Application of Generalized Inverses of Matrices », Symposium Proceedings, Texas Technological College Mathematics Series, no. 4, Lubbock, Texas (1968), pp. 1-25.
[20] Smogorshewsky, A., Les fonctions de Green des systèmes différentials linéaires dans un domaine à une seule dimension, Recueil Math., 7, 49, 179-196 (1940) · JFM 66.0422.01
[21] J. von Neumann,Functional Operators, vol. II:The Geometry of Orthogonal Spaces, Annals of Mathematical Studies, no. 22, Princeton (1950). · Zbl 0039.11701
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.