The Principal Symbol Map for Lagrangian Distributions with Complex Phase
G. Mattar (University of Goettingen)
TL;DR
This paper develops an alternative method to compute the principal symbol of Lagrangian distributions with complex phase, enhancing the analysis of Fourier integral operators in partial differential equations.
Contribution
It introduces a new construction of the principal symbol map that simplifies computation after composition of Fourier integral operators with complex phase.
Findings
Provides an explicit formula for the principal symbol after composition
Simplifies analysis of Fourier integral operators with complex phase
Enhances tools for PDE analysis involving complex phase Fourier integral operators
Abstract
Fourier integral operators with complex phase function are an important tool in the analysis of partial differential equations. The present paper focus on the principal symbol of Lagrangian distributions with complex phase. We provide an alternative construction of the principal symbol map for such distributions, which allows us to compute the principal symbol after clean composition of Fourier integral operators with complex phase.
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Taxonomy
Topicsadvanced mathematical theories · Algebraic and Geometric Analysis · Mathematical Analysis and Transform Methods