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Transactions of the American Mathematical Society

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Geometric aspects of Sturm-Liouville problems II. Space of boundary conditions for left-definiteness


Authors: Kevin Haertzen, Qingkai Kong, Hongyou Wu and Anton Zettl
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
Published electronically: August 21, 2003
MathSciNet review: 2020027
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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.


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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

DOI: https://doi.org/10.1090/S0002-9947-03-03028-9
Keywords: Regular Sturm-Liouville problems, left-definiteness, spaces of boundary conditions
Received by editor(s): November 16, 2001
Published electronically: August 21, 2003
Article copyright: © Copyright 2003 American Mathematical Society