Generalized boundary value problems with abstract side conditions and their adjoints. I

Brown, Richard C. ; Tvrdý, Milan

Czechoslovak Mathematical Journal, Tome 30 (1980) no. 1, pp. 7-27

Détail

DOI : 10.21136/CMJ.1980.101651

Classification : 34B05, 34G10, 47E05

Bibliographie

[1] Arens R.: Operational calculus of linear relations. Pacific J. Math. 11 (1961), 9-23. | DOI | MR | Zbl

[2] Brown R. C.: Duality theory for $n$-th order differential operators under Stieltjes boundary conditions. SIAM J. Math. Anal. 6 (1975), 882-900. | DOI | MR | Zbl

[3] Brown R. C.: Duality theory for $n$-th order differential operators under Stieltjes boundary conditions II: nonsmooth coefficients and nonsingular measures. Ann. di Mat. pura ed appl. 105 (1975), 141-170. | MR | Zbl

[4] Brown R. C.: Adjoint domains and generalized splines. Czech. Math. J. 25 (100), (1975), 134-147. | MR | Zbl

[5] Brown R. C.: The operator theory of generalized boundary value problems. Can. J. Math. 28 (1976), 486-512. | DOI | MR | Zbl

[6] Brown R. С., Krall A. M.: On minimizing the sum of squares of $L^2$ norms of differential operators under constraints. Czech. Math. J. 27 (102), (1977), 132-143. | MR

[7] Brown R. С., Krall A. M.: Ordinary differential operators under Stieltjes boundary conditions. Trans. Amer. Math. Soc. 198 (1970), 73 - 92. | DOI | MR

[8] Coddington E. A.: Extension theory of formally normal and symmetric subspaces. Mem. Amer. Soc. 134 (1973). | MR | Zbl

[9] Coddington E. A., Dijksma A.: Adjoint subspaces in Banach spaces with applications to ordinary differential subspaces. Ann. di Mat. pura ed appl. CXVIII (1978), 1 - 118. | MR | Zbl

[10] Dunford N., Schwartz J. T.: Linear Operators I. Interscience, New York (1957).

[11] Koldberg S.: Unbounded Linear Operators: Theory and applications. McGraw-Hill, New York (1966). | MR

[12] Hönig Ch. S.: Volterra-Stieltjes Integral Equations. Mathematics Studies 16, North-Holland, Amsterdam (1975). | MR

[13] Hönig Ch. S.: An unified representation theory for linear continuous operators between function spaces. to appear.

[14] Krall A. M.: Differential operators and their adjoints under integral and multiple point boundary conditions. J. Diff. Eq. 4 (1968), 327-336. | DOI | MR | Zbl

[15] Krall A. M.: Stieltjes differential-boundary operators III. Pacific J. Math., to appear. | MR | Zbl

[16] Krall A. M.: The development of general differential and general differential-boundary systems. Rocky Mountain J. Math. 5 (1975), 493 - 542. | DOI | MR | Zbl

[17] Krall A. M., Brown R. C.: $n$-th order differential systems under Stieltjes boundary conditions. MRC Tech. Summ. Rept # 1581.

[18] Luenberger D. G.: Optimization by Vector Space Methods. John Wiley, New York (1969). | MR | Zbl

[19] Parhimovič I. V.: Multipoint boundary value problems for linear integro-differential equations in a class of smooth functions. (in Russian), Diff. urav. 8 (1972), 549-552. | MR

[20] Pettis B. J.: On integration in vector spaces. Trans. Amer. Math. Soc. 44 (1938), 277-304. | DOI | MR | Zbl

[21] Rudin W.: Functional Analysis. Mc Graw-Hill (1973). | MR | Zbl

[22] Schwabik Š., Tvrdý M., Vejvoda O.: Differential and Integral Equations: Boundary Value Problems and Adjoints. Academia, Praha (1979). | MR

[23] Tvrdý M.: Boundary value problems for generalized linear differential equations and their adjoints. Czech. Math. J. 23 (98), (1973), 183-217. | MR

[24] Tvrdý M.: Boundary value problems for generalized linear integro-differential equations with left-continuous solutions. Čas. pěst. mat. 99 (1974), 147-157. | MR

[25] Tvrdý M.: Linear boundary value type problems for functional-differential equations and their adjoints. Czech. Math. J. 25 (100), (1975), 37-66. | MR

[26] Tvrdý M., Vejvoda O.: General boundary value problem for an integrodifferential system and its adjoint. Čas. pěst. mat. 97 (1972), 399-419 and 98 (1973), 26-42. | MR

[27] Vejvoda O., Tvrdý M.: Existence of solutions to a linear integro-boundary-diflferential equation with additional conditions. Ann. di Mat. pura ed appl. 89 (1971), 169-216. | MR

[28] Wexler D.: On boundary value problems for an ordinary differential system. Ann. di Mat. pura ed appl. 80 (1968), 123-134. | MR