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

作者：Binding Paul^*; Fleige Andreas

来源：Operators and Matrices, 2011, 5(4): 735-755.

DOI：10.7153/oam-05-52

• indefinite Sturm-Liouville problem
• Riesz basis
• HELP inequality

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.

• 出版日期2011-12