Non-Elliptic Quadratic Forms and Semiclassical Estimates for Non-selfadjoint Operators

Joseph Anthony Viola

doi:10.1093/imrn/rns188

Non-Elliptic Quadratic Forms and Semiclassical Estimates for Non-selfadjoint Operators

Joseph Anthony Viola

Mathematics (Faculty of Sciences)

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

Abstract

We consider a class of pseudodifferential operators with a doubly characteristic point, where the quadratic part of the symbol fails to be elliptic but obeys an averaging assumption. Under suitable additional assumptions, semiclassical resolvent estimates are established, where the modulus of the spectral parameter is allowed to grow slightly more rapidly than the semiclassical parameter.

Original language	English
Pages (from-to)	4615-4671
Journal	International Mathematics Research Notices
Issue number	20
DOIs	https://doi.org/10.1093/imrn/rns188
Publication status	Published - 2013

Subject classification (UKÄ)

Mathematical Sciences

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10.1093/imrn/rns188

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abstract = "We consider a class of pseudodifferential operators with a doubly characteristic point, where the quadratic part of the symbol fails to be elliptic but obeys an averaging assumption. Under suitable additional assumptions, semiclassical resolvent estimates are established, where the modulus of the spectral parameter is allowed to grow slightly more rapidly than the semiclassical parameter.",

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AB - We consider a class of pseudodifferential operators with a doubly characteristic point, where the quadratic part of the symbol fails to be elliptic but obeys an averaging assumption. Under suitable additional assumptions, semiclassical resolvent estimates are established, where the modulus of the spectral parameter is allowed to grow slightly more rapidly than the semiclassical parameter.

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DO - 10.1093/imrn/rns188

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JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 20

ER -

Non-Elliptic Quadratic Forms and Semiclassical Estimates for Non-selfadjoint Operators

Abstract

Subject classification (UKÄ)

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