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A Normal Form Around a Lagrangian Submanifold of Radial Points

Nick Haber

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Abstract

In this work, we produce microlocal normal forms for pseudodifferential operators which have a Lagrangian submanifold of radial points. This answers natural questions about such operators and their associated classical dynamics. In a sequel, we will give a microlocal parametrix construction, as well as a construction of a microlocal Poisson operator, for such pseudodifferential operators.

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What this paper is about

In this work, we produce microlocal normal forms for pseudodifferential operators which have a Lagrangian submanifold of radial points. This answers natural questions about such operators and their associated classical dynamics. In a sequel, we will give a microlocal parametrix construction, as well as a construction of a microlocal Poisson operator, for such pseudodifferential operators.

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Available abstract

In this work, we produce microlocal normal forms for pseudodifferential operators which have a Lagrangian submanifold of radial points. This answers natural questions about such operators and their associated classical dynamics. In a sequel, we will give a microlocal parametrix construction, as well as a construction of a microlocal Poisson operator, for such pseudodifferential operators.

Key concepts: Submanifold, Pseudodifferential operators, Mathematics, Parametrix, Microlocal analysis, Lagrangian, Operator (biology), Mathematical analysis

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