ON THE DENSITY OF THE WARD ANSATZE IN THE SPACE OF ANTI-SELF-DUAL YANG-MILLS SOLUTIONS - Ivancovich, J; Mason, L; Newman, E (Springer-Verlag, 1990)
A general patching matrix P for the twistor construction of antiself-dual Yang-Mills fields is approximated by a terminating Laurent series. The approximate patching matrix P(m) is triangularized (so that it becomes one of the Ward ansätze) and the associated Riemann-Hilbert problem is solved, thereby generating an anti-self-dual solution of the Yang-Mills equations. The approximate patching matrices and the associated (exact) anti-self-dual Yang-Mills solutions are then shown to converge on P and its corresponding solution so that the Ward ansätze forms a dense subset in the solution space in the Weierstrass sense. © 1990 Springer-Verlag.