Dispersive estimates for principally normal pseudodifferential operators

2004/01/19 by Herbert Koch, Daniel Tataru, Koch, Herbert +1 · 4 citations
Mathematics · #35B60 #35S05 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.AP #msc:35B60 #msc:35S05

paper · pdf · doi:10.48550/arxiv.math/0401234

72 pages

arxiv created 2004/01/19 · openalex publication_date 2004/01/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used to prove Carleman inequalities, which in turn yield unique continuation results for various partial differential operators with rough potentials.

Cited by

• Recent Results On The Modulated Cubic Nonlinear Schrödinger Equation On \mathbbT²
• Large data global well-posedness for the modified Novikov-Veselov system
• Sharp bilinear eigenfunction estimate, L^∞_x2L^p_t,x1-type Strichartz estimate, and energy-critical NLS
• Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation

Related

• Carleman estimates for third order operators of KdV and non KdV-type and applications
• Sparse bounds for pseudodifferential operators
• Dispersive estimates for Schroedinger operators: A survey
• A pseudodifferential Hormander's inequality
• Carleman estimates for a class of variable coefficient degenerate\n elliptic operators with applications to unique continuation