Fourier integrals and a new representation of Maslov's canonical operator near caustics

2013/07/08 by S. Yu. Dobrokhotov, Dobrokhotov, S. Yu., George N. Makrakis +5 · 1 citation
Mathematics · Physics and Astronomy · #35S30 (Secondary) #81Q20 (Primary) #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #advanced mathematical theories #math-ph #math.AP #math.MP #msc:35S30 #msc:81Q20

paper · pdf · doi:10.48550/arxiv.1307.2292

19 pages. Submitted to the Proceedings of the International Conference "Spectral Theory and Differential Equations (STDE-2012)" in honor of Vladimir A. Marchenko's 90th birthday, to be published by the AMS

arxiv created 2013/07/08 · openalex publication_date 2013/07/08 · arxiv updated 2013/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We suggest a new representation of Maslov's canonical operator in a neighborhood of the caustics using a special class of coordinate systems ("eikonal coordinates") on Lagrangian manifolds.

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• New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in 2D semiclassical asymptotics

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