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Differential Operators with Abstract Boundary Conditions

Published online by Cambridge University Press:  20 November 2018

R. C. Brown
R. C. Brown*
Affiliation:
The University of A labama, University, Alabama
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 2 , 01 April 1978 , pp. 262 - 288
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Arens, R., Operational calculus of linear relations, Pacific J. Math. 11 (1961), 9–23.Google Scholar
2. Brown, R. C., Adjoint domains and generalized splines, Czechoslovak Math. J. 25 (1975), 134–147.Google Scholar
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. Brown, R. C., The operator theory of generalized boundary value problems, Can. J. Math. 28 (1976), 486–512.Google Scholar
5. DeBoor, C., Row small can one make the derivative of an interpolating function, J. Approximation Theory IS (1975), 105–116.Google Scholar
6. DeBoor, C., On “best” interpolation J. Approximation Theory.Google Scholar
7. Dunford, N. and Schwartz, J. T., Linear operators, Part I (Interscience, New York, 1957).Google Scholar
8. Goldberg, S., Unbounded linear operators: Theory and applications (McGraw-Hill, New York, 1966).Google Scholar
9. Golomb, M., Hm-p extensions by Hm'p splines, J. Approximation Theory 5 (1972), 238–275.Google Scholar
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. Honig, C., Volterra-Stieltjes integral equations (North-Holland Math. Studies 16, (1975).Google Scholar
12. Jerome, J. W. and Schumaker, L. L., On Lq-splines, J. Approximation Theory 2 (1969), 24–49.Google Scholar
13. Krall, A. M., Differential boundary operators, Trans. Amer. Math. Soc. 154 (1971), 429–458.Google Scholar
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. Krall, A. M., Stieltjes differential-boundary operators III; multivalued operators, linear relations, Pacific J. Math. 59 (1975), 125–134.Google Scholar
16. Krall, A. M., order Stieltjes differential boundary operators and Stieltjes differential boundary systems, J. Differential Equations 24 (1977), 253–267.Google Scholar
17. Luenberger, D. G., Optimization by vector space methods (John Wiley, New York, 1969).Google Scholar
18. Reid, W. T., Ordinary linear differential operators of minimum norm, Duke Math. J. 29 (1962), 591–606.Google Scholar
19. Rudin, W., Functional analysis (McGraw-Hill, 1973).Google Scholar
20. Schoenberg, I. J., Cardinal spline interpolation, Vol. 12, CBMS Regional Conf. Series, SIAM, Philadelphia, 1973.Google Scholar
21. Tvrdy, M., Note on functional-differential equations with initial functions of bounded variation, Czech. Math. J. 25 (100) (1975), 67–70.Google Scholar