Ordinary Differential Operators under Stieltjes Boundary Conditions
نویسندگان
چکیده
The operator Lry = / + Py, whose domain is determined in part by the Stieltjes integral boundary condition Jo dv{i)y{f) = 0, is studied in Xj¡($>, 1), 1 < p < oo. It is shown that Lp has a dense domain; hence there exists a dual operator L* operating on .£¡¡(0,1). After finding LJ we show that both L, and L¡¡ are Fredholm operators. This implies some elementary results concerning the spectrum and states of Lp. Finally two eigenfunction expansions are derived.
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