On a sharp lemma of Cassels and Montgomery on manifolds

Brandolini, Luca; Gariboldi, Bianca Maria; Gigante, Giacomo

doi:10.1007/s00208-020-02115-0

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

Citazione:	(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
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:	MATHEMATISCHE ANNALEN
Nelle collezioni:	1.1.01 Articoli/Saggi in rivista - Journal Articles/Essays

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http://hdl.handle.net/10446/168638

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