Spherical Harmonics with Maximal Lp (2 < p ≤ 6) Norm Growth

Xiaolong Han*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)378-398
    Number of pages21
    JournalJournal of Geometric Analysis
    Volume26
    Issue number1
    DOIs
    Publication statusPublished - 1 Jan 2016

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