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Multilinear estimates for the Laplace spectral projectors on compact manifolds

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Title: Multilinear estimates for the Laplace spectral projectors on compact manifolds
Alternate Title: Estime´es multiline´aires pour les projecteurs spectraux du laplacien sur les varie´te´s compactes
Authors: Burq, Nicolas1 nicolas.burq@math.u-psud.fr, Gérard, Patrick1 Patrick.gerard@math.u-psud.fr, Tzvetkov, Nikolay1 nikolay.tzvetkov@math.u-psud.fr
Source: Comptes Rendus. Mathématique. Mar2004, Vol. 338 Issue 5, p359. 6p.
Subjects: Eigenfunctions, Numerical solutions to integral equations, Numerical solutions to boundary value problems, Numerical solutions to differential equations, Harmonic functions
Abstract (English): The purpose of this Note is to extend to any space dimension the bilinear estimate for eigenfunctions of the Laplace operator on a compact manifold (without boundary) obtained by the authors (preprint: http://www.arxiv.org/abs/math/0308214) in dimension 2. We also give some related trilinear estimates. To cite this article: N. Burq et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). [Copyright &y& Elsevier]
Abstract (French): L'objet de cette Note est de ge´ne´raliser a` toute dimension d'espace les estimations biline´aires de projecteurs spectraux de l'ope´rateur de Laplace sur une varie´te´ compacte (sans bord), de´montre´es par les auteurs (preprint : http://www.arxiv.org/abs/math/0308214) en dimension  2. On e´nonce aussi des estimations triline´aires. Pour citer cet article : N. Burq et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). [Copyright 2004 Elsevier]
Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 12308011
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Multilinear estimates for the Laplace spectral projectors on compact manifolds
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  Data: Estime´es multiline´aires pour les projecteurs spectraux du laplacien sur les varie´te´s compactes
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  Data: <searchLink fieldCode="AR" term="%22Burq%2C+Nicolas%22">Burq, Nicolas</searchLink><relatesTo>1</relatesTo><i> nicolas.burq@math.u-psud.fr</i><br /><searchLink fieldCode="AR" term="%22Gérard%2C+Patrick%22">Gérard, Patrick</searchLink><relatesTo>1</relatesTo><i> Patrick.gerard@math.u-psud.fr</i><br /><searchLink fieldCode="AR" term="%22Tzvetkov%2C+Nikolay%22">Tzvetkov, Nikolay</searchLink><relatesTo>1</relatesTo><i> nikolay.tzvetkov@math.u-psud.fr</i>
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  Data: <searchLink fieldCode="JN" term="%22Comptes+Rendus%2E+Mathématique%22">Comptes Rendus. Mathématique</searchLink>. Mar2004, Vol. 338 Issue 5, p359. 6p.
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  Data: <searchLink fieldCode="DE" term="%22Eigenfunctions%22">Eigenfunctions</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+integral+equations%22">Numerical solutions to integral equations</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+boundary+value+problems%22">Numerical solutions to boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+differential+equations%22">Numerical solutions to differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Harmonic+functions%22">Harmonic functions</searchLink>
– Name: Abstract
  Label: Abstract (English)
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  Data: The purpose of this Note is to extend to any space dimension the bilinear estimate for eigenfunctions of the Laplace operator on a compact manifold (without boundary) obtained by the authors (preprint: http://www.arxiv.org/abs/math/0308214) in dimension <f>2</f>. We also give some related trilinear estimates. To cite this article: N. Burq et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). [Copyright &y& Elsevier]
– Name: Abstract
  Label: Abstract (French)
  Group: Ab
  Data: L'objet de cette Note est de ge´ne´raliser a` toute dimension d'espace les estimations biline´aires de projecteurs spectraux de l'ope´rateur de Laplace sur une varie´te´ compacte (sans bord), de´montre´es par les auteurs (preprint : http://www.arxiv.org/abs/math/0308214) en dimension  2. On e´nonce aussi des estimations triline´aires. Pour citer cet article : N. Burq et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). [Copyright 2004 Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        PageCount: 6
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      – SubjectFull: Eigenfunctions
        Type: general
      – SubjectFull: Numerical solutions to integral equations
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      – SubjectFull: Numerical solutions to boundary value problems
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      – SubjectFull: Numerical solutions to differential equations
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      – TitleFull: Multilinear estimates for the Laplace spectral projectors on compact manifolds
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