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This work explores the analytic theory behind the quadratic scattering wave front set, focusing on its properties and applications in areas like microlocal analysis and mathematical physics. We delve into the underlying mathematical structures and provide a comprehensive analysis of this important concept, aiming to further understanding and utilization within relevant fields.

Explore the fascinating mathematical structures formed by pseudodifferential operators, which constitute essential algebras in functional analysis. These operator algebras provide powerful tools for studying partial differential equations and are fundamental in areas like microlocal analysis.