Geometric aspects of Sturm-Liouville problems II. Space of boundary conditions for left-definiteness
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- by Kevin Haertzen, Qingkai Kong, Hongyou Wu and Anton Zettl PDF
- Trans. Amer. Math. Soc. 356 (2004), 135-157 Request permission
Abstract:
For a given regular Sturm-Liouville equation with an indefinite weight function, we explicitly describe the space of left-definite selfadjoint boundary conditions. The description only uses one value of a fundamental solution of the matrix form of the equation. As a consequence we show that this space has the shape of a solid consisting of two cones sharing a common base.References
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Additional Information
- Kevin Haertzen
- Affiliation: Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115
- Qingkai Kong
- Affiliation: Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115
- Hongyou Wu
- Affiliation: Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115
- Anton Zettl
- Affiliation: Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115
- Received by editor(s): November 16, 2001
- Published electronically: August 21, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 356 (2004), 135-157
- MSC (2000): Primary 34B24, 34B09; Secondary 34L05, 34L15
- DOI: https://doi.org/10.1090/S0002-9947-03-03028-9
- MathSciNet review: 2020027