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

Haertzen, Kevin; Kong, Qingkai; Wu, Hongyou; Zettl, Anton

doi:10.1090/S0002-9947-03-03028-9

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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