Fourier coefficients of restrictions of eigenfunctions
Fourier coefficients of restrictions of eigenfunctions
复制标题
特征函数的傅里叶限制系数
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
S. Zelditch
中科院分区：
文献类型：
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作者：
E. Wyman;Yakun Xi;S. Zelditch
Let {ej} be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold (M, g). Let H ⊂ M be a submanifold and {ψk} be an orthonormal basis of Laplace eigenfunctions of H with the induced metric. We obtain joint asymptotics for the Fourier coefficients 〈γHej,ψk〉L2(H)=∫Hejψ¯kdVHdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${leftlangle {{gamma _H}{e_j},{psi _k}}
ight
angle _{{L^2}(H)}} = {int_H {{e_j}overline psi } _k}d{V_H}$$end{document} of restrictions γhej of ej to H. In particular, we obtain asymptotics for the sums of the norm-squares of the Fourier coefficients over the joint spectrum {(μk,λj)}j,k−0∞documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$left{ {({mu _k},{lambda _j})}
ight}_{j,k - 0}^infty $$end{document} of the (square roots of the) Laplacian ΔM on M and the Laplacian ΔH on H in a family of suitably ‘thick’ regions in ℝ2. Thick regions include (1) the truncated cone μk/λj ∈ [a, b] ⊂ (0, 1) and λj ≼ λ, and (2) the slowly thickening strip ∣μk − cλj∣ ≼ w(λ) and λj ⩼ λ, where w(λ) is monotonic and 1 ≪ w(λ) ≾ λ1/2. Key tools for obtaining the asymptotics include the composition calculus of Fourier integral operators and a new multidimensional Tauberian theorem.
影响因子：
3.1
作者：
Canzani, Yaiza;Galkowski, Jeffrey
通讯作者：
Galkowski, Jeffrey