## Ordinary differential operators under Stieltjes boundary conditions

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- by Richard C. Brown and Allan M. Krall
- Trans. Amer. Math. Soc.
**198**(1974), 73-92 - DOI: https://doi.org/10.1090/S0002-9947-1974-0358436-2
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## Abstract:

The operator ${L_p}y = y’ + Py$, whose domain is determined in part by the Stieltjes integral boundary condition $\int _0^1 {d\nu (t)y(t) = 0}$, is studied in $\mathcal {L}_n^p(0,1),1 \leqslant p < \infty$. It is shown that ${L_p}$ has a dense domain; hence there exists a dual operator $L_q^ +$ operating on $\mathcal {L}_n^q(0,1)$. After finding $L_q^ +$ we show that both ${L_p}$ and $L_q^ +$ are Fredholm operators. This implies some elementary results concerning the spectrum and states of ${L_p}$. Finally two eigenfunction expansions are derived.## References

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## Bibliographic Information

- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**198**(1974), 73-92 - MSC: Primary 47E05; Secondary 34B10
- DOI: https://doi.org/10.1090/S0002-9947-1974-0358436-2
- MathSciNet review: 0358436