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Perturbation of a Sturm-Liouville Operator by a Finite Function

1965
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Proceedings of the American Mathematical Society
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If Fi is a self-adjoint operator and F is a bounded self-adjoint operator in a Hilbert space and if F2=Fi-|-F, then Theorem 1 of [2] states that Here Ri(z) is the resolvent of F¿, || ||2 is the Schmidt norm, and 5 stands for trace. From (1) various trace formulas for differential operators may be obtained. In [2] the condition (2) was verified for the situation in which Fi is defined in L2 [0, oe ) by the ordinary differential operator L= -D2 and the boundary condition w(0) = 0, and V is the

doi:10.2307/2033914
fatcat:iiq3ztpyarcelfeiuv4wq22h5m