Zeros of the Wronskian and Renormalized Oscillation Theory
نویسندگان
چکیده
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 = Ejuj , 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.
منابع مشابه
ZEROS OF THE WRONSKIAN AND RENORMALIZED OSCILLATION THEORY By F. GESZTESY, B. SIMON, and G. TESCHL
For general Sturm-Liouville operators with separated boundary conditions, we prove the following: If E1,2 2 R and if u1,2 solve the differential equation Huj = Ejuj, 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.
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