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Adjoints of multipoint-integral boundary value problems


Authors: R. C. Brown and Allan M. Krall
Journal: Proc. Amer. Math. Soc. 37 (1973), 213-216
MSC: Primary 47E05; Secondary 34B05
DOI: https://doi.org/10.1090/S0002-9939-1973-0308856-1
MathSciNet review: 0308856
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Abstract: The dual system to $ Ly = y' + Py$,

$\displaystyle \sum\limits_{i = 0}^\infty {{A_i}y({t_i}) + \int_0^1 {K(t)y(t)\;dt = 0} } $

is found when the setting is $ L_n^p(0,1),1 < p < \infty $.

References [Enhancements On Off] (What's this?)

  • [1] R. C. Brown, The existence of the adjoint in linear differential systems with discontinuous boundary conditions, Ann. Mat. Pura Appl. (to appear). MR 0315236 (47:3785)
  • [2] R. N. Bryan, A linear differential system with general linear boundary conditions, J. Differential Equations 5 (1969), 38-48. MR 38 #1312. MR 0232989 (38:1312)
  • [3] S. Goldberg, Unbounded linear operators: Theory and applications, McGraw-Hill, New York, 1966. MR 34 #580. MR 0200692 (34:580)
  • [4] G. B. Green and A. M. Krall, Linear differential systems with infinitely many boundary points, Ann. Mat. Pura Appl. 91 (1972), 53-67. MR 0316805 (47:5353)
  • [5] A. M. Krall, Differential-boundary operators, Trans. Amer. Math. Soc. 154 (1971), 429-458. MR 42 #6328. MR 0271445 (42:6328)

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DOI: https://doi.org/10.1090/S0002-9939-1973-0308856-1
Article copyright: © Copyright 1973 American Mathematical Society

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