An application of symbol calculus

Emmanuel Andronikof

A chapter in New Trends in Microlocal Analysis, 1997, pp 159-164 from Springer

Abstract: 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 = t =ξ1 = … = ξτ = 0, τ ≠ 0, is a quotient of a system of the form (tD t − A(x, D x ))u = D x1 u = … = D xτu = 0, with A essentially of order ≤ 0.

Keywords: Holomorphic Function; Conjugacy Class; Order Zero; Distribution Solution; Regular System (search for similar items in EconPapers)
Date: 1997
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-68413-8_12

Ordering information: This item can be ordered from
http://www.springer.com/9784431684138

DOI: 10.1007/978-4-431-68413-8_12

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().