On the remainder in the Weyl formula for the Euclidean disk

Yves Colin de Verdière[1]

  • [1] Institut Fourier, Unité mixte de recherche CNRS-UJF 5582, BP 74, 38402-Saint Martin d’Hères Cedex (France)

Séminaire de théorie spectrale et géométrie (2010-2011)

  • Volume: 29, page 1-13
  • ISSN: 1624-5458

Abstract

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We prove a 2-terms Weyl formula for the counting function N ( μ ) of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimate O μ 2 / 3 .

How to cite

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Colin de Verdière, Yves. "On the remainder in the Weyl formula for the Euclidean disk." Séminaire de théorie spectrale et géométrie 29 (2010-2011): 1-13. <http://eudml.org/doc/219821>.

@article{ColindeVerdière2010-2011,
abstract = {We prove a 2-terms Weyl formula for the counting function $N(\mu )$ of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimate $O\left(\mu ^\{2/3\}\right)$.},
affiliation = {Institut Fourier, Unité mixte de recherche CNRS-UJF 5582, BP 74, 38402-Saint Martin d’Hères Cedex (France)},
author = {Colin de Verdière, Yves},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {lattice point problem; Laplace operator; eigenvalues; Weyl asymptotic formula; Bessel functions},
language = {eng},
pages = {1-13},
publisher = {Institut Fourier},
title = {On the remainder in the Weyl formula for the Euclidean disk},
url = {http://eudml.org/doc/219821},
volume = {29},
year = {2010-2011},
}

TY - JOUR
AU - Colin de Verdière, Yves
TI - On the remainder in the Weyl formula for the Euclidean disk
JO - Séminaire de théorie spectrale et géométrie
PY - 2010-2011
PB - Institut Fourier
VL - 29
SP - 1
EP - 13
AB - We prove a 2-terms Weyl formula for the counting function $N(\mu )$ of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimate $O\left(\mu ^{2/3}\right)$.
LA - eng
KW - lattice point problem; Laplace operator; eigenvalues; Weyl asymptotic formula; Bessel functions
UR - http://eudml.org/doc/219821
ER -

References

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