Am. J. Math. 118, 571-594 (1996) [DOI: 10.1353/ajm.1996.0024]

Zeros of the Wronskian and Renormalized Oscillation Theory

Fritz Gesztesy, Barry Simon, and Gerald Teschl

For general Sturm-Liouville operators with separated boundary conditions, we prove the following: If E1,2∈ℝ and if u1,2 solve the differential equation Huj=Ej uj, j=1,2 and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection P(E1, E2)(H) of H equals the number of zeros of the Wronskian of u1 and u2.

MSC91: Primary 34B24, 34C10; Secondary 34L15, 34L05
Keywords: Oscillation theory, Sturm-Liouville operators, eigenvalues

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