Scientific article
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M operators: a generalisation of Weyl–Titchmarsh theory

Published inJournal of computational and applied mathematics, vol. 171, no. 1, p. 1-26
Publication date2004

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.

Citation (ISO format)
AMREIN, Werner, PEARSON, Doran. <i>M</i> operators: a generalisation of Weyl–Titchmarsh theory. In: Journal of computational and applied mathematics, 2004, vol. 171, n° 1, p. 1–26. doi: 10.1016/j.cam.2004.01.020
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ISSN of the journal0377-0427

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