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Acta Applicandae Mathematica

, Volume 92, Issue 3, pp 241–267 | Cite as

A Banach Algebra Version of the Sato Grassmannian and Commutative Rings of Differential Operators

  • Maurice J. DupréEmail author
  • James F. Glazebrook
  • Emma Previato
Article
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Abstract

We show that commutative rings of formal pseudodifferential operators can be conjugated as subrings in noncommutative Banach algebras of operators in the presence of certain eigenfunctions. Techniques involve those of the Sato Grassmannian as used in the study of the KP hierarchy as well as the geometry of an infinite dimensional Stiefel bundle with structure modeled on such Banach algebras. Generalizations of this procedure are also considered.

Key words

semigroup Fredholm operator Sato Grassmannian KP hierarchy Burchnall–Chaundy ring iterated Laurent series 

Mathematics Subject Classifications (2000)

37K30 35Q53 58F37 58B25 
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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  • Maurice J. Dupré
    • 1
    Email author
  • James F. Glazebrook
    • 2
    • 3
  • Emma Previato
    • 4
    • 5
  1. 1.Department of MathematicsTulane UniversityNew OrleansUSA
  2. 2.Department of Mathematics and Computer ScienceEastern Illinois UniversityCharlestonUSA
  3. 3.Department of MathematicsUniversity of Illinois at Urbana–ChampaignUrbanaUSA
  4. 4.Institut Mittag–LefflerThe Royal Swedish Academy of SciencesDjursholmSweden
  5. 5.Department of MathematicsBoston UniversityBostonUSA

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