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This paper develops a local analogue of the ADHM construction, whichcharacterises ASD instantons defined over smooth bounded domains insideEuclidean $\mathbb{R}^4$ diffeomorphic to the 4-ball, in terms of infinitedimensional Hilbert spaces and bounded Hermitian linear operators satisfying ananalogue of the ADHM equation. Morever, we describe the degeneration of thisconstruction when a family of instantons develops a curvature singularity atthe origin.

Local Nahm transform and singularity formation of ASD connections