Let (M,g) be a d-dimensional compact connected Riemannian manifold and let {φ_m}, m=0,...,+oo, be a complete sequence of orthonormal eigenfunctions of the Laplace–Beltrami operator on M. We show that there exists a positive constant C such that for all integers N and X and for all finite sequences of N points in M, {x(j)}, and positive weights {a_j}, j=1,...N, we have ∑|∑a_j φ_m(x(j)|^2 ≥ max (C X∑a_j^2, (∑a_j)^2), (in the left-hand side the inner sum is for j=1,...,N and the outer sum is for m=0,...,X).
(2020). On a sharp lemma of Cassels and Montgomery on manifolds [journal article - articolo]. In MATHEMATISCHE ANNALEN. Retrieved from http://hdl.handle.net/10446/168638
Titolo: | On a sharp lemma of Cassels and Montgomery on manifolds |
Tipologia specifica: | articolo |
Tutti gli autori: | Brandolini, Luca; Gariboldi, Bianca; Gigante, Giacomo |
Data di pubblicazione: | 2020-11-21 |
Abstract (eng): | Let (M,g) be a d-dimensional compact connected Riemannian manifold and let {φ_m}, m=0,...,+oo, be a complete sequence of orthonormal eigenfunctions of the Laplace–Beltrami operator on M. We show that there exists a positive constant C such that for all integers N and X and for all finite sequences of N points in M, {x(j)}, and positive weights {a_j}, j=1,...N, we have ∑|∑a_j φ_m(x(j)|^2 ≥ max (C X∑a_j^2, (∑a_j)^2), (in the left-hand side the inner sum is for j=1,...,N and the outer sum is for m=0,...,X). |
Rivista: | |
Nelle collezioni: | 1.1.01 Articoli/Saggi in rivista - Journal Articles/Essays |
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