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An application of symbol calculus

  • Emmanuel Andronikof

Abstract

Let X = ℂ t,x 1+n , t ∈ ℂ, x = (x 1,…,x n ) ∈ ℂ n , and let (t, x; τ,ξ)) be the associated symplectic coordinates in T*X. In Kashiwara and Oshima’s study of regular systems (cf [5]), the following definition occurs (with a slightly different vocabulary): a matrix of microdifferential operators A(x,D x ) is essentially of order ≥ 0 if there exists ν > 0 such that the coefficients of any power of A are microdifferential operators of order at most v. It is shown in [5] that any regular system of microdifferential equations with regular singularities along V = t1 = … = ξτ = 0, τ ≠ 0, is a quotient of a system of the form (tD t A(x, D x ))u = D x1 u = … = D u = 0, with A essentially of order ≤ 0.

Keywords

Holomorphic Function Conjugacy Class Order Zero Distribution Solution Regular System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Tokyo 1997

Authors and Affiliations

  • Emmanuel Andronikof

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