Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418570 | Journal of Mathematical Analysis and Applications | 2014 | 15 Pages |
Abstract
Connections between different areas of mathematical analysis are obtained: regular variation, indefinite operator theory and HELP type inequalities. Using a result by Parfyonov, the nondecreasing and so-called positively increasing functions induce precisely those indefinite KreÄn-Feller eigenvalue problems such that the eigenfunctions have the Riesz basis property. Furthermore, these functions induce precisely those Lebesgue-Stieltjes measures such that the associated HELP type inequalities are valid. The so-called dual KreÄn-Feller eigenvalue problems allow a similar characterization of the class of nondecreasing O-regularly varying functions.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Andreas Fleige,