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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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