0-th Order Pseudo-differential Operator on the Circle

2019/09/13 by Zhongkai Tao, Tao, Zhongkai · 3 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.AP #math.SP

paper · pdf · doi:10.48550/arxiv.1909.06316

arxiv created 2019/09/13 · openalex publication_date 2019/09/13 · arxiv updated 2019/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider 0-th order pseudodifferential operators on the circle. We show that inside any interval disjoint from critical values of the principal symbol, the spectrum is absolutely continuous with possibly finitely many embedded eigenvalues. We also give an example of embedded eigenvalues.

Cited by

• Long-time evolution of forced waves in the low viscosity regime
• The scattering matrix for 0th order pseudodifferential operators
• Discrete spectrum of zero order pseudodifferential operators

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