M operators: a generalisation of Weyl

Article Article scientifique Article M operators: a generalisation of Weyl–Titchmarsh theory eng 2004 author Amrein Werner 24807 author Pearson Doran 82666 1-26 10.1016/j.cam.2004.01.020 0377-0427 The theory of the Weyl-Titchmarsh m function for second-order ordinary differential operators in generalized and applied to partial differential operators of the form - Δ + q(x) acting in three space dimensions. Weyl operators M(z) are defined as maps from L2 (S1) to L2 (S1) (S1 ≡ unit sphere in R3) for exterior and interior boundary value problems, and for the partial differential operator acting in L2 (R3), with the standard Weyl-Titchmarsh m function recovered in the special case that q is spherically symmetric. The analysis is carried out rather explicity, allowing for the determination of precise norm bounds for M operators and for the proof of higher dimensional analogues of a number of the fundamental results of standard Weyl-Titchmarsh theory. Dewey 510 25 Section de mathématiques 11 false Journal of computational and applied mathematics 171 1 f5098ea5-17c0-4bad-8ffa-32a60a7caef9 Article (Published version) Public Amrein_JCAM_200426.pdf 543690 application/pdf eb80f5bd0e6b6a6beae79e14737f5d28a7a05fa20954baa2a44b104ebdc7b007 openAccess Faculté des sciences / Section de mathématiques

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M operators: a generalisation of Weyl–Titchmarsh theory	Journal of computational and applied mathematics			2004	94	742

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Pearson, Doran