Invariant subspaces of elliptic systems I: Pseudodifferential projections

Capoferri, Matteo ORCID: https://orcid.org/0000-0001-6226-1407 and Vassiliev, Dmitri 2022. Invariant subspaces of elliptic systems I: Pseudodifferential projections. Journal of Functional Analysis 282 (8) , 109402. 10.1016/j.jfa.2022.109402

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Abstract

Consider an elliptic self-adjoint pseudodifferential operator A acting on m-columns of half-densities on a closed manifold M, whose principal symbol is assumed to have simple eigenvalues. We show existence and uniqueness of m orthonormal pseudodifferential projections commuting with the operator A and provide an algorithm for the computation of their full symbols, as well as explicit closed formulae for their subprincipal symbols. Pseudodifferential projections yield a decomposition of into invariant subspaces under the action of A modulo . Furthermore, they allow us to decompose A into m distinct sign definite pseudodifferential operators. Finally, we represent the modulus and the Heaviside function of the operator A in terms of pseudodifferential projections and discuss physically meaningful examples.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0022-1236
Funders:	Leverhulme Trust
Date of First Compliant Deposit:	9 February 2022
Date of Acceptance:	13 January 2022
Last Modified:	18 Nov 2023 17:48
URI:	https://orca.cardiff.ac.uk/id/eprint/147338

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