The blowup along the diagonal of the spectral function of the Laplacian

We formulate a precise conjecture about the universal behavior near the diagonal of the spectral function of the Laplacian of a smooth compact Riemann manifold. We prove this conjecture when the manifold and the metric are real analytic.

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Bibliographic Details
Published inBollettino della Unione matematica italiana (2008) Vol. 9; no. 3; pp. 411 - 420
Main Author Nicolaescu, Liviu I.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2016
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Riemann manifold
Spectral function
33C45
Harmonic polynomials
Real analytic manifolds
58J50
Eigenfunctions
35J15
Riemann manifolds
Laplacian
32C05
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Summary:We formulate a precise conjecture about the universal behavior near the diagonal of the spectral function of the Laplacian of a smooth compact Riemann manifold. We prove this conjecture when the manifold and the metric are real analytic.
ISSN:1972-6724
2198-2759
DOI:10.1007/s40574-016-0055-3