Differential Operators with Abstract Boundary Conditions

Brown, R. C.

Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 262-288

Résumé

Suppose F is a topological vector space. Let ACm ≡ ACm[a, b] be the absolutely continuous m-dimensional vector valued functions y on the compact interval [a, b] with essentially bounded components. Consider the boundary value problem (1.1) where A0, A are respectively... operator with range in F.

Détail

DOI : 10.4153/CJM-1978-025-2

Bibliographie

[1] 1. Arens, R., Operational calculus of linear relations, Pacific J. Math. 11 (1961), 9–23. Google Scholar

[2] 2. Brown, R. C., Adjoint domains and generalized splines, Czechoslovak Math. J. 25 (1975), 134–147. Google Scholar

[3] 3. Brown, R. C., Duality theory for nth order differential operators under Stieltjes boundary conditions II: nonsmooth coefficients and nonsingular measures, Ann. Math. Pura. Appl. 105 (1975), 141–170. Google Scholar

[4] 4. Brown, R. C., The operator theory of generalized boundary value problems, Can. J. Math. 28 (1976), 486–512. Google Scholar

[5] 5. DeBoor, C., Row small can one make the derivative of an interpolating function, J. Approximation Theory IS (1975), 105–116. Google Scholar

[6] 6. DeBoor, C., On “best” interpolation J. Approximation Theory. Google Scholar

[7] 7. Dunford, N. and Schwartz, J. T., Linear operators, Part I (Interscience, New York, 1957). Google Scholar

[8] 8. Goldberg, S., Unbounded linear operators: Theory and applications (McGraw-Hill, New York, 1966). Google Scholar

[9] 9. Golomb, M., Hm-p extensions by Hm'p splines, J. Approximation Theory 5 (1972), 238–275. Google Scholar

[10] 10. Henry, D., The adjoint of a linear functional differential equation and boundary value problems, J. Differential Equations 9 (1971), 55–66. Google Scholar

[11] 11. Honig, C., Volterra-Stieltjes integral equations (North-Holland Math. Studies 16, (1975). Google Scholar

[12] 12. Jerome, J. W. and Schumaker, L. L., On Lq-splines, J. Approximation Theory 2 (1969), 24–49. Google Scholar

[13] 13. Krall, A. M., Differential boundary operators, Trans. Amer. Math. Soc. 154 (1971), 429–458. Google Scholar

[14] 14. Krall, A. M., The development of general differential and general differential-boundary systems, Rocky Mountain J. Math. 5 (1975), 493–542. Google Scholar

[15] 15. Krall, A. M., Stieltjes differential-boundary operators III; multivalued operators, linear relations, Pacific J. Math. 59 (1975), 125–134. Google Scholar

[16] 16. Krall, A. M., order Stieltjes differential boundary operators and Stieltjes differential boundary systems, J. Differential Equations 24 (1977), 253–267. Google Scholar

[17] 17. Luenberger, D. G., Optimization by vector space methods (John Wiley, New York, 1969). Google Scholar

[18] 18. Reid, W. T., Ordinary linear differential operators of minimum norm, Duke Math. J. 29 (1962), 591–606. Google Scholar

[19] 19. Rudin, W., Functional analysis (McGraw-Hill, 1973). Google Scholar

[20] 20. Schoenberg, I. J., Cardinal spline interpolation, Vol. 12, CBMS Regional Conf. Series, SIAM, Philadelphia, 1973. Google Scholar

[21] 21. Tvrdy, M., Note on functional-differential equations with initial functions of bounded variation, Czech. Math. J. 25 (100) (1975), 67–70. Google Scholar