TY - JOUR
T1 - The Kernel Bundle of a Holomorphic Fredholm Family
AU - Krainer, Thomas
AU - Mendoza, Gerardo A.
N1 - Funding Information:
Work partially supported by the National Science Foundation, Grants DMS-0901202 and DMS-0901173.
PY - 2013/12
Y1 - 2013/12
N2 - 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.
AB - 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.
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U2 - 10.1080/03605302.2013.818017
DO - 10.1080/03605302.2013.818017
M3 - Article
AN - SCOPUS:84887028786
SN - 0360-5302
VL - 38
SP - 2107
EP - 2125
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 12
ER -