Stieltjes differential-boundary operators

Krall, Allan M.

doi:10.1090/S0002-9939-1973-0320415-3

Stieltjes differential-boundary operators
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by Allan M. Krall PDF

Proc. Amer. Math. Soc. 41 (1973), 80-86 Request permission

Abstract:

The differential-boundary system $S$: \[ Ly = (y + H(t)[Cy(0) + Dy(1)] + {H_1}(t)\psi )’ + P(t)y.\] \[ Ay(0) + By(1) + \int _0^1 {dK(t)y(t) = 0} ,\quad \int _0^1 {d{K_1}(t)y(t)} = 0,\] 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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