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C*-algebras of singular integral operators on the line related to singular Sturm-Liouville problems

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Abstract

We study certain C*-algebras of singular integral operators on the line related to the second order ordinary differential operators Ho=-d/dx p(x) d/dx + q(x), with smooth coefficients and domain C ∞o (ℝ) on L2(IR). Using Gelfand theory we find the structure of such algebras and deduce Fredholm criteria for related classes of ordinary differential operators of all orders. We give a complete description of some special cases including the case where p=l and where q≥1 is an even polynomial of arbitrary even degree.

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  1. Department of Mathematics, University of Kansas, 66045, Lawrence, Ks., USA

    Houshang H. Sohrab

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  1. Houshang H. Sohrab
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Sohrab, H.H. C*-algebras of singular integral operators on the line related to singular Sturm-Liouville problems. Manuscripta Math 41, 109–138 (1983). https://doi.org/10.1007/BF01165931

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