Abstract
This paper develops a local analogue of the ADHM construction, which characterises ASD instantons defined over smooth bounded domains inside Euclidean mathbb {R}^4 diffeomorphic to the 4-ball, in terms of infinite dimensional Hilbert spaces and bounded Hermitian linear operators satisfying an analogue of the ADHM equation. Morever, we describe the degeneration of this construction when a family of instantons develops a curvature singularity at the origin.
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