Symbolic Functional Calculus and N-Body Resolvent Estimates

Andrew Hassell; András Vasy

doi:10.1006/jfan.2000.3569

Symbolic Functional Calculus and N-Body Resolvent Estimates

Andrew Hassell^*, András Vasy

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

We construct a functional calculus for symbolic functions of "scattering pseudodifferential operators" on manifolds with boundary. This is applied to obtain mapping results on the scattering wavefront set of the B operator used by Gérard et al. (1994, "Commutator Algebra and Resolvent Estimates," Advanced Studies in Pure Mathematics, Vol. 23, Math. Soc. Japan, Tokyo) to obtain N-body resolvent estimates. As an application, we construct the plane waves for an N-body, short range Schrödinger operator and obtain a scattering wavefront set estimate.

Original language	English
Pages (from-to)	257-283
Number of pages	27
Journal	Journal of Functional Analysis
Volume	173
Issue number	2
DOIs	https://doi.org/10.1006/jfan.2000.3569
Publication status	Published - 1 Jun 2000

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abstract = "We construct a functional calculus for symbolic functions of {"}scattering pseudodifferential operators{"} on manifolds with boundary. This is applied to obtain mapping results on the scattering wavefront set of the B operator used by G{\'e}rard et al. (1994, {"}Commutator Algebra and Resolvent Estimates,{"} Advanced Studies in Pure Mathematics, Vol. 23, Math. Soc. Japan, Tokyo) to obtain N-body resolvent estimates. As an application, we construct the plane waves for an N-body, short range Schr{\"o}dinger operator and obtain a scattering wavefront set estimate.",

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author = "Andrew Hassell and Andr{\'a}s Vasy",

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AU - Hassell, Andrew

AU - Vasy, András

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N2 - We construct a functional calculus for symbolic functions of "scattering pseudodifferential operators" on manifolds with boundary. This is applied to obtain mapping results on the scattering wavefront set of the B operator used by Gérard et al. (1994, "Commutator Algebra and Resolvent Estimates," Advanced Studies in Pure Mathematics, Vol. 23, Math. Soc. Japan, Tokyo) to obtain N-body resolvent estimates. As an application, we construct the plane waves for an N-body, short range Schrödinger operator and obtain a scattering wavefront set estimate.

AB - We construct a functional calculus for symbolic functions of "scattering pseudodifferential operators" on manifolds with boundary. This is applied to obtain mapping results on the scattering wavefront set of the B operator used by Gérard et al. (1994, "Commutator Algebra and Resolvent Estimates," Advanced Studies in Pure Mathematics, Vol. 23, Math. Soc. Japan, Tokyo) to obtain N-body resolvent estimates. As an application, we construct the plane waves for an N-body, short range Schrödinger operator and obtain a scattering wavefront set estimate.

KW - Functional calculus; pseudodifferential operators; scattering calculus; N-body problem; plane waves

UR - https://www.scopus.com/pages/publications/0000059859

U2 - 10.1006/jfan.2000.3569

DO - 10.1006/jfan.2000.3569

M3 - Article

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VL - 173

SP - 257

EP - 283

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Symbolic Functional Calculus and N-Body Resolvent Estimates

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