Zeros of the Wronskian and renormalized oscillation theory

Type: Article

Publication Date: 1996-06-01

Citations: 78

DOI: https://doi.org/10.1353/ajm.1996.0024

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 j u 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 .

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