Improved time-decay for a class of scaling critical electromagnetic Schrödinger flows

2015/02/17 by Luca Fanelli, Gabriele Grillo, Fanelli, Luca +4
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.AP #math.SP

paper · pdf · doi:10.48550/arxiv.1502.04987

arxiv created 2015/02/17 · openalex publication_date 2015/02/17 · arxiv updated 2015/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a Schrödinger hamiltonian H(A,a) with scaling critical and time independent external electromagnetic potential, and assume that the angular operator L associated to H is positive definite. We prove the following: if ‖e^-itH(A,a)‖_{L¹→ L^∞}\lesssim t^-n/2, then ‖|x|^-g(n)e^-itH(A,a)|x|^-g(n)‖_{L¹→ L^∞}\lesssim t^-n/2-g(n), g(n) being a positive number, explicitly depending on the ground level of L and the space dimension n. We prove similar results also for the heat semi-group generated by H(A,a).

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