Sharp L → L Bounds on Spectral Projectors for Low Regularity Metrics
نویسنده
چکیده
We establish L2 → Lq mapping bounds for unit-width spectral projectors associated to elliptic operators with Cs coefficients, in the case 1 ≤ s ≤ 2. Examples of Smith-Sogge [6] show that these bounds are best possible for q less than the critical index. We also show that L∞ bounds hold with the same exponent as in the case of smooth coefficients.
منابع مشابه
Sharp L Bounds on Spectral Clusters for Holder Metrics
We establish Lq bounds on eigenfunctions, and more generally on spectrally localized functions (spectral clusters), associated to a self-adjoint elliptic operator on a compact manifold, under the assumption that the coefficients of the operator are of regularity Cs, where 0 ≤ s ≤ 1. We also produce examples which show that these bounds are best possible for the case q =∞, and for 2 ≤ q ≤ qn.
متن کاملSharp Bounds on the PI Spectral Radius
In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.
متن کاملSpectrality of Ordinary Differential Operators
We prove the long standing conjecture in the theory of two-point boundary value problems that completeness and Dunford’s spectrality imply Birkhoff regularity. In addition we establish the even order part of S.G.Krein’s conjecture that dissipative differential operators are Birkhoff-regular and give sharp estimate of the norms of spectral projectors in the odd case. Considerations are based on ...
متن کاملSubcritical L Bounds on Spectral Clusters for Lipschitz Metrics
We establish asymptotic bounds on the Lp norms of spectrally localized functions in the case of two-dimensional Dirichlet forms with coefficients of Lipschitz regularity. These bounds are new for the range 6 < p < ∞. A key step in the proof is bounding the rate at which energy spreads for solutions to hyperbolic equations with Lipschitz coefficients.
متن کاملar X iv : 0 70 9 . 27 64 v 1 [ m at h . A P ] 1 8 Se p 20 07 SUBCRITICAL L p BOUNDS ON SPECTRAL CLUSTERS FOR LIPSCHITZ METRICS
We establish asymptotic bounds on the L norms of spectrally localized functions in the case of two-dimensional Dirichlet forms with coefficients of Lipschitz regularity. These bounds are new for the range 6 < p < ∞. A key step in the proof is bounding the rate at which energy spreads for solutions to hyperbolic equations with Lipschitz coefficients.
متن کامل