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https://hdl.handle.net/2440/88599
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Type: | Journal article |
Title: | Improvement of eigenfunction estimates on manifolds of nonpositive curvature |
Author: | Hassell, A. Tacy, M. |
Citation: | Forum Mathematicum, 2013; 27(3):1435-1451 |
Publisher: | De Gruyter |
Issue Date: | 2013 |
ISSN: | 0933-7741 1435-5337 |
Statement of Responsibility: | Andrew Hassell, Melissa Tracy |
Abstract: | Let (M,g) be a compact, boundaryless manifold of dimension n with the property that either (i) n = 2 and (M,g) has no conjugate points, or (ii) the sectional curvatures of (M,g) are nonpositive. Let Δ be the positive Laplacian on M determined by g. We study the L2 → Lp mapping properties of a spectral cluster of (Δ)1/2 of width 1/log λ. Under the geometric assumptions above, Bérard [Math. Z. 155 (1977), 249–276] obtained a logarithmic improvement for the remainder term of the eigenvalue counting function which directly leads to a (log λ)1/2 improvement for Hörmander's estimate on the L∞ norms of eigenfunctions. In this paper we extend this improvement to the Lp estimates for all p > 2(n+1)/(n-1). |
Keywords: | Eigenfunction estimates nonpositive curvature manifolds without conjugate points logarithmic improvement finite propagation speed |
Description: | Published Online: 2013-04-03 |
Rights: | © de Gruyter 2015 |
DOI: | 10.1515/forum-2012-0176 |
Grant ID: | http://purl.org/au-research/grants/arc/FT0990895 http://purl.org/au-research/grants/arc/DP1095448 http://purl.org/au-research/grants/arc/DP120102019 |
Published version: | http://dx.doi.org/10.1515/forum-2012-0176 |
Appears in Collections: | Aurora harvest 2 Mathematical Sciences publications |
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