Spectral theory of translation surfaces : A short introduction

Luc Hillairet[1]

  • [1] Université de Nantes Laboratoire de mathématiques Jean Leray UMR CNRS 6629 2 rue de la Houssinière BP 92208 44322 Nantes cedex 3 (France)

Séminaire de théorie spectrale et géométrie (2009-2010)

  • Volume: 28, page 51-62
  • ISSN: 1624-5458

Abstract

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We define translation surfaces and, on these, the Laplace operator that is associated with the Euclidean (singular) metric. This Laplace operator is not essentially self-adjoint and we recall how self-adjoint extensions are chosen. There are essentially two geometrical self-adjoint extensions and we show that they actually share the same spectrum

How to cite

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Hillairet, Luc. "Spectral theory of translation surfaces : A short introduction." Séminaire de théorie spectrale et géométrie 28 (2009-2010): 51-62. <http://eudml.org/doc/116465>.

@article{Hillairet2009-2010,
abstract = {We define translation surfaces and, on these, the Laplace operator that is associated with the Euclidean (singular) metric. This Laplace operator is not essentially self-adjoint and we recall how self-adjoint extensions are chosen. There are essentially two geometrical self-adjoint extensions and we show that they actually share the same spectrum},
affiliation = {Université de Nantes Laboratoire de mathématiques Jean Leray UMR CNRS 6629 2 rue de la Houssinière BP 92208 44322 Nantes cedex 3 (France)},
author = {Hillairet, Luc},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {translation surfaces; flat Laplace operator; isospectrality},
language = {eng},
pages = {51-62},
publisher = {Institut Fourier},
title = {Spectral theory of translation surfaces : A short introduction},
url = {http://eudml.org/doc/116465},
volume = {28},
year = {2009-2010},
}

TY - JOUR
AU - Hillairet, Luc
TI - Spectral theory of translation surfaces : A short introduction
JO - Séminaire de théorie spectrale et géométrie
PY - 2009-2010
PB - Institut Fourier
VL - 28
SP - 51
EP - 62
AB - We define translation surfaces and, on these, the Laplace operator that is associated with the Euclidean (singular) metric. This Laplace operator is not essentially self-adjoint and we recall how self-adjoint extensions are chosen. There are essentially two geometrical self-adjoint extensions and we show that they actually share the same spectrum
LA - eng
KW - translation surfaces; flat Laplace operator; isospectrality
UR - http://eudml.org/doc/116465
ER -

References

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