The Kernel Bundle of a Holomorphic Fredholm Family

Thomas Krainer, Gerardo A. Mendoza

Research output: Contribution to journalArticle

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Abstract

Let Y{script} be a smooth connected manifold, Σ ⊂ ℂ an open set and (σ, y) → P{script}y(σ) a family of unbounded Fredholm operators D ⊂ H 1 → H 2 of index 0 depending smoothly on (y, σ) ∈ Y{script} × Σ and holomorphically on σ. We show how to associate to P{script}, under mild hypotheses, a smooth vector bundle K{script} → Y{script} whose fiber over a given y ∈ Y{script} consists of classes, modulo holomorphic elements, of meromorphic elements φ with P{script}yφ holomorphic. As applications we give two examples relevant in the general theory of boundary value problems for elliptic wedge operators.

Original languageEnglish (US)
Pages (from-to)2107-2125
Number of pages19
JournalCommunications in Partial Differential Equations
Volume38
Issue number12
DOIs
Publication statusPublished - Dec 1 2013

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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