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Spectral Pollution and How to Avoid It (With Applications to Dirac and Periodic Schrödinger Operators)

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Academic year: 2021

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Table 1. Summary of our results from Section 2.3 for the Dirac operator D 0 + V , when a splitting is imposed on the Hilbert space L 2 ( R 3 , C 4 ).
Table 2. Summary of our results for the Dirac operator D 0 + V when a balance is imposed between vectors of the basis.
Fig. 1. For an operator A which has a spectral gap [a, b] in its essential spectrum, pollution can occur in the whole gap.
Fig. 2. Illustration of Theorem 2.1: for an operator A with a gap [a, b] in its essential spectrum, pollution can occur in the whole gap, except between the convex hulls of ˆσ ess A | PH

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