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Published June 1996 | Published
Journal Article Open

Zeros of the Wronskian and Renormalized Oscillation Theory

Abstract

For general Sturm-Liouville operators with separated boundary conditions, we prove the following: If E_(1,2) ∈ R and if u_(1,2) solve the differential equation Hu_j = E_ju_j, j = 1, 2 and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection P(E_1,E_2)(H) of H equals the number of zeros of the Wronskian of u_1 and u_2.

Additional Information

© 1995 Johns Hopkins University Press. Manuscript received May 3, 1995; revised August 16, 1995. Research supported in part by NSF Grant DMS-9401491.

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August 18, 2023
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