On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem

Boris Sternin

Open Mathematics (2011)

  • Volume: 9, Issue: 4, page 814-832
  • ISSN: 2391-5455

Abstract

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We consider a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold. Ellipticity condition and Fredholm property for elliptic operators are obtained. This class of operators is studied using pseudodifferential uniformization, which reduces the problem to a pseudodifferential operator acting in sections of infinite-dimensional bundles.

How to cite

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Boris Sternin. "On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem." Open Mathematics 9.4 (2011): 814-832. <http://eudml.org/doc/269578>.

@article{BorisSternin2011,
abstract = {We consider a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold. Ellipticity condition and Fredholm property for elliptic operators are obtained. This class of operators is studied using pseudodifferential uniformization, which reduces the problem to a pseudodifferential operator acting in sections of infinite-dimensional bundles.},
author = {Boris Sternin},
journal = {Open Mathematics},
keywords = {G-pseudodifferential operators; Transversal ellipticity; Pseudodifferential uniformization; Lie groups; Finiteness theorem; -pseudodifferential operators; transversal ellipticity; pseudodifferential uniformization; finiteness theorem},
language = {eng},
number = {4},
pages = {814-832},
title = {On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem},
url = {http://eudml.org/doc/269578},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Boris Sternin
TI - On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem
JO - Open Mathematics
PY - 2011
VL - 9
IS - 4
SP - 814
EP - 832
AB - We consider a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold. Ellipticity condition and Fredholm property for elliptic operators are obtained. This class of operators is studied using pseudodifferential uniformization, which reduces the problem to a pseudodifferential operator acting in sections of infinite-dimensional bundles.
LA - eng
KW - G-pseudodifferential operators; Transversal ellipticity; Pseudodifferential uniformization; Lie groups; Finiteness theorem; -pseudodifferential operators; transversal ellipticity; pseudodifferential uniformization; finiteness theorem
UR - http://eudml.org/doc/269578
ER -

References

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