Sturm–Liouville problems with indefinite weights and Everitt's inequality
Copyright policy )Sturm–Liouville problems with indefinite weights and Everitt's inequality
It is shown that spectral properties of Sturm–Liouville eigenvalue problems with indefinite weights are related to integral inequalities studied by Everitt. A result of Beals on indefinite problems leads to a sufficient condition for the validity of such an inequality. A Baire category argument is used to show that, in general, the inequality under consideration does not hold.
- University of Wisconsin–Milwaukee United States
- University of Wisconsin System United States
Sturm-Liouville theory, completeness of eigenfunctions, Hardy-Littlewood-Pólya type integral inequality, integral inequalities, Sturm-Liouville problems, Riesz basis, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
Sturm-Liouville theory, completeness of eigenfunctions, Hardy-Littlewood-Pólya type integral inequality, integral inequalities, Sturm-Liouville problems, Riesz basis, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
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