Improved Spectral Cluster Bounds for Orthonormal Systems

2023/07/21 by Ren, Tianyi, Zhang, An · 2 citations
#35P15 #58J50 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.11597

Abstract

We improve Frank-Sabin's work concerning the spectral cluster bounds for orthonormal systems at p=∞, on the flat torus and spaces of nonpositive sectional curvature, by shrinking the spectral band from [λ², (λ+1)²) to [λ², (λ+ε(λ))²), where ε(λ) is a function of λ that goes to 0 as λ goes to ∞. In achieving this, we invoke the method developed by Bourgain-Shao-Sogge-Yao.

Cited by

• Strichartz estimates involving orthonormal systems at the critical summability exponent
• Orthonormal Strichartz estimates for Dunkl-Schrödinger equation of initial data with Sobolev regularity

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