Exponential coordinates and regularity of groupoid heat kernels

Bing So

Open Mathematics (2014)

  • Volume: 12, Issue: 2, page 284-297
  • ISSN: 2391-5455

Abstract

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We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.

How to cite

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Bing So. "Exponential coordinates and regularity of groupoid heat kernels." Open Mathematics 12.2 (2014): 284-297. <http://eudml.org/doc/269786>.

@article{BingSo2014,
abstract = {We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.},
author = {Bing So},
journal = {Open Mathematics},
keywords = {Groupoid; Heat kernel; Singular differential operators; singular differential operators; pseudo-differential operators on differential groupoids; groupoid heat kernels},
language = {eng},
number = {2},
pages = {284-297},
title = {Exponential coordinates and regularity of groupoid heat kernels},
url = {http://eudml.org/doc/269786},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Bing So
TI - Exponential coordinates and regularity of groupoid heat kernels
JO - Open Mathematics
PY - 2014
VL - 12
IS - 2
SP - 284
EP - 297
AB - We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.
LA - eng
KW - Groupoid; Heat kernel; Singular differential operators; singular differential operators; pseudo-differential operators on differential groupoids; groupoid heat kernels
UR - http://eudml.org/doc/269786
ER -

References

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  6. [6] Melrose R.B., The Atiyah-Patodi-Singer Index Theorem, Res. Notes in Math., 4, A K Peters, Wellesley, 1993 Zbl0796.58050
  7. [7] Nistor V., Groupoids and integration of Lie algebroids, J. Math. Soc. Japan, 2000, 52(4), 847–868 http://dx.doi.org/10.2969/jmsj/05240847 Zbl0965.58023
  8. [8] Nistor V., Weinstein A., Xu P., Pseudodifferential operators on differential groupoids, Pacific J. Math., 1999, 189(1), 117–152 http://dx.doi.org/10.2140/pjm.1999.189.117 Zbl0940.58014
  9. [9] So B.K., Pseudo-Differential Operators, Heat Calculus and Index Theory of Groupoids Satisfying the Lauter-Nistor Condition, PhD thesis, University of Warwick, Warwick, 2010 
  10. [10] So B.K., On the full calculus of pseudo-differential operators on boundary groupoids with polynomial growth, Adv. Math., 2013, 237, 1–32 http://dx.doi.org/10.1016/j.aim.2013.01.001 Zbl1269.58007

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