Transactions of the American Mathematical Society

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

Author(s): Kevin Haertzen; Qingkai Kong; Hongyou Wu; Anton Zettl
Journal: Trans. Amer. Math. Soc. 356 (2004), 135-157.
MSC (2000): Primary 34B24, 34B09; Secondary 34L05, 34L15
Posted: August 21, 2003
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 34B24, 34B09, 34L05, 34L15

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: 10.1090/S0002-9947-03-03028-9
PII: S 0002-9947(03)03028-9
Keywords: Regular Sturm-Liouville problems, left-definiteness, spaces of boundary conditions
Received by editor(s): November 16, 2001
Posted: August 21, 2003
Copyright of article: Copyright 2003, American Mathematical Society

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ISSN 1088-6850(e) ISSN 0002-9947(p)

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