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The Kernel Bundle of a Holomorphic Fredholm Family
Krainer, T Mendoza, GA
Krainer, T
Mendoza, GA
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Journal Article
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2013-12-01
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10.1080/03605302.2013.818017
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. © 2013 Copyright Taylor and Francis Group, LLC.
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Informa UK Limited
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Communications in Partial Differential Equations
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