GROWTH OF HIGH LP NORMS FOR EIGENFUNCTIONS AN APPLICATION OF GEODESIC BEAMS

被引:0
|
作者
Canzani, Yaiza [1 ]
Galkowski, Jeffrey [2 ]
机构
[1] Univ North Carolina Chapel Hill, Dept Math, Chapel Hill, NC 27599 USA
[2] UCL, Dept Math, London, England
来源
ANALYSIS & PDE | 2023年 / 16卷 / 10期
基金
美国国家科学基金会;
关键词
Eigenfunctions; high energy; Lp norms; microlocal; second microlocal; L-P-NORMS; KAKEYA-NIKODYM BOUNDS; RIEMANNIAN-MANIFOLDS; NODAL SETS; IMPROVEMENTS; QUASIMODES; AVERAGES;
D O I
10.2140/apde.2023.16.2267
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
[Hezari and Riviere 2016] H. Hezari and G. Riviere, "Lp norms, nodal sets, and quantum ergodicity", Adv. Math. 290 (2016), 938-966. MR Zbl [Koch et al. 2007] H. Koch, D. Tataru, and M. Zworski, "Semiclassical Lp estimates", Ann. Henri Poincare 8:5 (2007), 885-916. MR Zbl [Lee 2013] J. M. Lee, Introduction to smooth manifolds, 2nd ed., Grad. Texts in Math. 218, Springer, 2013. MR Zbl [Sjostrand and Zworski 1999] J. Sjostrand and M. Zworski, "Asymptotic distribution of resonances for convex obstacles", Acta Math. 183:2 (1999), 191-253. MR Zbl [Sogge 1988] C. D. Sogge, "Concerning the Lp norm of spectral clusters for second-order elliptic operators on compact manifolds", J. Funct. Anal. 77:1 (1988), 123-138. MR Zbl [Sogge and Zelditch 2002] C. D. Sogge and S. Zelditch, "Riemannian manifolds with maximal eigenfunction growth", Duke Math. J. 114:3 (2002), 387-437. MR Zbl [Sogge and Zelditch 2016] C. D. Sogge and S. Zelditch, "A note on Lp-norms of quasi-modes", pp. 385-397 in Some topics in harmonic analysis and applications, edited by J. Li et al., Adv. Lect. Math. 34, Int. Press, Somerville, MA, 2016. MR Zbl [Sogge et al. 2011] C. D. Sogge, J. A. Toth, and S. Zelditch, "About the blowup of quasimodes on Riemannian manifolds", J. Geom. Anal. 21:1 (2011), 150-173. MR Zbl [Tacy 2018] M. Tacy, "A note on constructing families of sharp examples for Lp growth of eigenfunctions and quasimodes", Proc. Amer. Math. Soc. 146:7 (2018), 2909-2924. MR Zbl [Tacy 2019] M. Tacy, "Lp estimates for joint quasimodes of semiclassical pseudodifferential operators", Israel J. Math. 232:1 (2019), 401-425. MR Zbl [Toth and Zelditch 2002] J. A. Toth and S. Zelditch, "Riemannian manifolds with uniformly bounded eigenfunctions", Duke Math. J. 111:1 (2002), 97-132. MR Zbl [Toth and Zelditch 2003] J. A. Toth and S. Zelditch, "Lp norms of eigenfunctions in the completely integrable case", Ann. Henri Poincare 4:2 (2003), 343-368. MR Zbl [Zworski 2012] M. Zworski, Semiclassical analysis, Grad. Stud. in Math. 138, Amer. Math. Soc., Providence, RI, 2012. MR Zbl
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页码:2267 / 2325
页数:62
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