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Consider the indefinite Sturm-Liouville problem−f ′′ = λrf, f(−1) = f(1) = 0 with an indefinite weight function r ∈ L[−1, 1] satisfying xr(x) > 0. A number of conditions for the so-called Riesz basis property are reviewed, i.e. conditions such that the eigenfunctions form a Ries basis of the Hilbert space L|r|[−1, 1]. Most of these conditions were previously known to be either necessary or sufficient (or both if r is odd). Now it is shown that all are equivalent to the Riesz basis property if r is strongly odd dominated, i.e. the even part of r is dominated by the odd part in some sense. One of the equivalent conditions is the validity of the HELP-type inequality on [0, 1] (∫ 1

A review of a Riesz basis property for indefinite Sturm-Liouville problems