A Shubin Pseudodifferential Calculus on Asymptotically Conic Manifolds

Thomas Krainer

doi:10.1007/s00041-025-10178-3

A Shubin Pseudodifferential Calculus on Asymptotically Conic Manifolds

Thomas Krainer

Division of Mathematics & Natural Sciences (Altoona)

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

Abstract

We present a global pseudodifferential calculus on asymptotically conic manifolds that generalizes (anisotropic versions of) Shubin’s classical global pseudodifferential calculus on Euclidean space to this class of noncompact manifolds. Fully elliptic operators are shown to be Fredholm in an associated scale of Sobolev spaces, and to have parametrices in the calculus.

Original language	English (US)
Article number	44
Journal	Journal of Fourier Analysis and Applications
Volume	31
Issue number	3
DOIs	https://doi.org/10.1007/s00041-025-10178-3
State	Published - Jun 2025

All Science Journal Classification (ASJC) codes

Analysis
General Mathematics
Applied Mathematics

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10.1007/s00041-025-10178-3

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abstract = "We present a global pseudodifferential calculus on asymptotically conic manifolds that generalizes (anisotropic versions of) Shubin{\textquoteright}s classical global pseudodifferential calculus on Euclidean space to this class of noncompact manifolds. Fully elliptic operators are shown to be Fredholm in an associated scale of Sobolev spaces, and to have parametrices in the calculus.",

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AB - We present a global pseudodifferential calculus on asymptotically conic manifolds that generalizes (anisotropic versions of) Shubin’s classical global pseudodifferential calculus on Euclidean space to this class of noncompact manifolds. Fully elliptic operators are shown to be Fredholm in an associated scale of Sobolev spaces, and to have parametrices in the calculus.

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A Shubin Pseudodifferential Calculus on Asymptotically Conic Manifolds

Abstract

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