We show that the space of Sturm-Liouville operators characterized by H
= (q, α,
β) ∈ L1(0,1)×[0,π)2
such that ò01 q = 0 is
homeomorphic to the partition set of the space of all admissible sequence X = {X
k(n)} which form sequences that converge to some q,
α, and
β individually. This space
Γ of quasinodal sequences is a superset of,
and is more natural than the space of asymptotically equivalent nodal sequences
described in earlier paper by Law-Tsay. The proof relies on the L1
convergence of the reconstruction formula for q by the exactly nodal
sequence. The result is a direct generalization of that in Law-Tsay.
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