| Title:
|
Generalized boundary value problems with abstract side conditions and their adjoints. I (English) |
| Author:
|
Brown, Richard C. |
| Author:
|
Tvrdý, Milan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
30 |
| Issue:
|
1 |
| Year:
|
1980 |
| Pages:
|
7-(27) |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
34B05 |
| MSC:
|
34G10 |
| MSC:
|
47E05 |
| idZBL:
|
Zbl 0454.47025 |
| idMR:
|
MR565904 |
| DOI:
|
10.21136/CMJ.1980.101651 |
| . |
| Date available:
|
2008-06-09T14:37:10Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101651 |
| . |
| Reference:
|
[1] Arens R.: Operational calculus of linear relations.Pacific J. Math. 11 (1961), 9-23. Zbl 0102.10201, MR 0123188, 10.2140/pjm.1961.11.9 |
| Reference:
|
[2] Brown R. C.: Duality theory for $n$-th order differential operators under Stieltjes boundary conditions.SIAM J. Math. Anal. 6 (1975), 882-900. Zbl 0316.47027, MR 0385224, 10.1137/0506077 |
| Reference:
|
[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. Zbl 0316.47027, MR 0422745 |
| Reference:
|
[4] Brown R. C.: Adjoint domains and generalized splines.Czech. Math. J. 25 (100), (1975), 134-147. Zbl 0309.41014, MR 0397243 |
| Reference:
|
[5] Brown R. C.: The operator theory of generalized boundary value problems.Can. J. Math. 28 (1976), 486-512. Zbl 0338.34008, MR 0412899, 10.4153/CJM-1976-050-4 |
| Reference:
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[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 0430395 |
| Reference:
|
[7] Brown R. С., Krall A. M.: Ordinary differential operators under Stieltjes boundary conditions.Trans. Amer. Math. Soc. 198 (1970), 73 - 92. MR 0358436, 10.1090/S0002-9947-1974-0358436-2 |
| Reference:
|
[8] Coddington E. A.: Extension theory of formally normal and symmetric subspaces.Mem. Amer. Soc. 134 (1973). Zbl 0265.47023, MR 0477855 |
| Reference:
|
[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. Zbl 0408.47035, MR 0533601 |
| Reference:
|
[10] Dunford N., Schwartz J. T.: Linear Operators I.Interscience, New York (1957). |
| Reference:
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[11] Koldberg S.: Unbounded Linear Operators: Theory and applications.McGraw-Hill, New York (1966). MR 0200692 |
| Reference:
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[12] Hönig Ch. S.: Volterra-Stieltjes Integral Equations.Mathematics Studies 16, North-Holland, Amsterdam (1975). MR 0499969 |
| Reference:
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[13] Hönig Ch. S.: An unified representation theory for linear continuous operators between function spaces.to appear. |
| Reference:
|
[14] Krall A. M.: Differential operators and their adjoints under integral and multiple point boundary conditions.J. Diff. Eq. 4 (1968), 327-336. Zbl 0165.42702, MR 0230968, 10.1016/0022-0396(68)90019-3 |
| Reference:
|
[15] Krall A. M.: Stieltjes differential-boundary operators III.Pacific J. Math., to appear. Zbl 0294.34006, MR 0372316 |
| Reference:
|
[16] Krall A. M.: The development of general differential and general differential-boundary systems.Rocky Mountain J. Math. 5 (1975), 493 - 542. Zbl 0322.34009, MR 0409946, 10.1216/RMJ-1975-5-4-493 |
| Reference:
|
[17] Krall A. M., Brown R. C.: $n$-th order differential systems under Stieltjes boundary conditions.MRC Tech. Summ. Rept # 1581. |
| Reference:
|
[18] Luenberger D. G.: Optimization by Vector Space Methods.John Wiley, New York (1969). Zbl 0176.12701, MR 0238472 |
| Reference:
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[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 0298370 |
| Reference:
|
[20] Pettis B. J.: On integration in vector spaces.Trans. Amer. Math. Soc. 44 (1938), 277-304. Zbl 0019.41603, MR 1501970, 10.1090/S0002-9947-1938-1501970-8 |
| Reference:
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[21] Rudin W.: Functional Analysis.Mc Graw-Hill (1973). Zbl 0253.46001, MR 0365062 |
| Reference:
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[22] Schwabik Š., Tvrdý M., Vejvoda O.: Differential and Integral Equations: Boundary Value Problems and Adjoints.Academia, Praha (1979). MR 0542283 |
| Reference:
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[23] Tvrdý M.: Boundary value problems for generalized linear differential equations and their adjoints.Czech. Math. J. 23 (98), (1973), 183-217. MR 0320417 |
| Reference:
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[24] Tvrdý M.: Boundary value problems for generalized linear integro-differential equations with left-continuous solutions.Čas. pěst. mat. 99 (1974), 147-157. MR 0405041 |
| Reference:
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[25] Tvrdý M.: Linear boundary value type problems for functional-differential equations and their adjoints.Czech. Math. J. 25 (100), (1975), 37-66. MR 0374609 |
| Reference:
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[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 0320672 |
| Reference:
|
[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 0316988 |
| Reference:
|
[28] Wexler D.: On boundary value problems for an ordinary differential system.Ann. di Mat. pura ed appl. 80 (1968), 123-134. MR 0247242 |
| . |
