Abstract
In this paper, we show that there exists a positive density subsequence of orthonormal spherical harmonics which achieves the maximal Lp norm growth for 2<p≤6, therefore giving an example of a Riemannian surface supporting such a subsequence of eigenfunctions. This answers the question proposed by Sogge and Zelditch (Concerning the L4 Norms of Typical Eigenfunctions on Compact Surfaces. Recent Developments in Geometry and Analysis, Int. Press, Somerville, pp. 407–423, 2012). Furthermore, we provide an explicit lower bound on the density in this example.
Original language | English |
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Pages (from-to) | 378-398 |
Number of pages | 21 |
Journal | Journal of Geometric Analysis |
Volume | 26 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2016 |