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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Stieltjes differential-boundary operators


Author: Allan M. Krall
Journal: Proc. Amer. Math. Soc. 41 (1973), 80-86
MSC: Primary 34B05
MathSciNet review: 0320415
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Abstract: The differential-boundary system $ S$:

$\displaystyle Ly = (y + H(t)[Cy(0) + Dy(1)] + {H_1}(t)\psi )' + P(t)y.$

$\displaystyle Ay(0) + By(1) + \int_0^1 {dK(t)y(t) = 0} ,\quad \int_0^1 {d{K_1}(t)y(t)} = 0,$

is discussed when set in the space $ \mathcal{L}_n^p[0,1]$. The density of the domain of $ L$ is discussed, and the adjoint or dual operator is derived. A discussion of selfadjoint systems follows. Necessary and sufficient conditions for $ T = (1/i)L$ to be selfadjoint in $ \mathcal{L}_n^2[0,1]$ are given.

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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0320415-3
Keywords: Operator, differential operator, adjoint operator
Article copyright: © Copyright 1973 American Mathematical Society