A REVIEW OF A RIESZ BASIS PROPERTY FOR INDEFINITE STURM-LIOUVILLE PROBLEMS

For an indefinite weight function r on [-1, 1] with xr(x) > 0 we consider connections between a Riesz basis property of the indefinite Sturm-Liouville eigenvalue problem -y '' = lambda ry, y(-1) = y(1) = 0 and various different conditions, for example HELP-type inequalities (integral(1)(0)vertical bar h'vertical bar(2)1/rdx)(2) <= k(integral(1)(0)vertical bar h vertical bar(2)dx) (integral(1)(0)vertical bar h'/r)' vertical bar(2)dx) for certain classes of functions h on [0, 1]. We show that for so-called strongly odd dominated functions r (including odd r) these problems are equivalent. This allows us to apply known results from the theory of one problem to the others.