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

Richard C. Brown; Milan Tvrdý

Czechoslovak Mathematical Journal (1980)

  • Volume: 30, Issue: 1, page 7-(27)
  • ISSN: 0011-4642

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Brown, Richard C., and Tvrdý, Milan. "Generalized boundary value problems with abstract side conditions and their adjoints. I." Czechoslovak Mathematical Journal 30.1 (1980): 7-(27). <http://eudml.org/doc/13172>.

@article{Brown1980,
author = {Brown, Richard C., Tvrdý, Milan},
journal = {Czechoslovak Mathematical Journal},
keywords = {generalized boundary value problem; adjoint; Fredholm alternative},
language = {eng},
number = {1},
pages = {7-(27)},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized boundary value problems with abstract side conditions and their adjoints. I},
url = {http://eudml.org/doc/13172},
volume = {30},
year = {1980},
}

TY - JOUR
AU - Brown, Richard C.
AU - Tvrdý, Milan
TI - Generalized boundary value problems with abstract side conditions and their adjoints. I
JO - Czechoslovak Mathematical Journal
PY - 1980
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 30
IS - 1
SP - 7
EP - (27)
LA - eng
KW - generalized boundary value problem; adjoint; Fredholm alternative
UR - http://eudml.org/doc/13172
ER -

References

top
  1. Arens R., 10.2140/pjm.1961.11.9, Pacific J. Math. 11 (1961), 9-23. (1961) Zbl0102.10201MR0123188DOI10.2140/pjm.1961.11.9
  2. Brown R. C., 10.1137/0506077, SIAM J. Math. Anal. 6 (1975), 882-900. (1975) Zbl0316.47027MR0385224DOI10.1137/0506077
  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. (1975) Zbl0316.47027MR0422745
  4. Brown R. C., Adjoint domains and generalized splines, Czech. Math. J. 25 (100), (1975), 134-147. (1975) Zbl0309.41014MR0397243
  5. Brown R. C., 10.4153/CJM-1976-050-4, Can. J. Math. 28 (1976), 486-512. (1976) Zbl0338.34008MR0412899DOI10.4153/CJM-1976-050-4
  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. (1977) Zbl0369.34007MR0430395
  7. Brown R. С., Krall A. M., 10.1090/S0002-9947-1974-0358436-2, Trans. Amer. Math. Soc. 198 (1970), 73 - 92. (198) Zbl0295.34010MR0358436DOI10.1090/S0002-9947-1974-0358436-2
  8. Coddington E. A., Extension theory of formally normal and symmetric subspaces, Mem. Amer. Soc. 134 (1973). (1973) Zbl0265.47023MR0477855
  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. (1978) Zbl0408.47035MR0533601
  10. Dunford N., Schwartz J. T., Linear Operators I, Interscience, New York (1957). (1957) Zbl0084.10402
  11. Koldberg S., Unbounded Linear Operators: Theory and applications, McGraw-Hill, New York (1966). (1966) MR0200692
  12. Hönig Ch. S., Volterra-Stieltjes Integral Equations, Mathematics Studies 16, North-Holland, Amsterdam (1975). (1975) MR0499969
  13. Hönig Ch. S., An unified representation theory for linear continuous operators between function spaces, to appear. 
  14. Krall A. M., 10.1016/0022-0396(68)90019-3, J. Diff. Eq. 4 (1968), 327-336. (1968) Zbl0165.42702MR0230968DOI10.1016/0022-0396(68)90019-3
  15. Krall A. M., Stieltjes differential-boundary operators III, Pacific J. Math., to appear. Zbl0294.34006MR0372316
  16. Krall A. M., 10.1216/RMJ-1975-5-4-493, Rocky Mountain J. Math. 5 (1975), 493 - 542. (1975) Zbl0322.34009MR0409946DOI10.1216/RMJ-1975-5-4-493
  17. Krall A. M., Brown R. C., n -th order differential systems under Stieltjes boundary conditions, MRC Tech. Summ. Rept # 1581. Zbl0369.34006
  18. Luenberger D. G., Optimization by Vector Space Methods, John Wiley, New York (1969). (1969) Zbl0176.12701MR0238472
  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. (1972) MR0298370
  20. Pettis B. J., 10.1090/S0002-9947-1938-1501970-8, Trans. Amer. Math. Soc. 44 (1938), 277-304. (1938) Zbl0019.41603MR1501970DOI10.1090/S0002-9947-1938-1501970-8
  21. Rudin W., Functional Analysis, Mc Graw-Hill (1973). (1973) Zbl0253.46001MR0365062
  22. Schwabik Š., Tvrdý M., Vejvoda O., Differential and Integral Equations: Boundary Value Problems and Adjoints, Academia, Praha (1979). (1979) Zbl0417.45001MR0542283
  23. Tvrdý M., Boundary value problems for generalized linear differential equations and their adjoints, Czech. Math. J. 23 (98), (1973), 183-217. (1973) Zbl0267.45013MR0320417
  24. Tvrdý M., Boundary value problems for generalized linear integro-differential equations with left-continuous solutions, Čas. pěst. mat. 99 (1974), 147-157. (1974) Zbl0293.45011MR0405041
  25. Tvrdý M., Linear boundary value type problems for functional-differential equations and their adjoints, Czech. Math. J. 25 (100), (1975), 37-66. (1975) Zbl0328.34071MR0374609
  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. (1972) Zbl0246.45012MR0320672
  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. (1971) Zbl0233.34022MR0316988
  28. Wexler D., On boundary value problems for an ordinary differential system, Ann. di Mat. pura ed appl. 80 (1968), 123-134. (1968) Zbl0175.09502MR0247242

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