The Corona Theorem for Slice Hyperholomorphic Functions of a Quaternionic Variable
A proof that the Corona problem holds for slice hyperholomorphic functions of a single quaternionic variable, the first such result in a hypercomplex setting. The quaternionic Bezout equation, taken with respect to the closed slice product, is reformulated as a system of Bezout equations on the unit disc and solved by adapting Wolff's proof of the classical Corona theorem, handling one, two and finally arbitrarily many generators.
2501.00543
This paper resolves the Corona problem in the quaternionic slice hyperholomorphic setting, the first treatment of the Corona problem within a hypercomplex framework. Because pointwise multiplication …