Criteria for the strong regularity of J -inner functions and γ -generating matrices

The class of left and right strongly regular J -inner mvf’s plays an important role in bitangential interpolation problems and in bitangential direct and inverse problems for canonical systems of integral and differential equations. A new criterion for membership in this class is presented in terms of the matricial Muckenhoupt condition (A2) that was introduced for other purposes by Treil and Volberg. Analogous results are also obtained for the class of γ -generating functions that intervene in the Nehari problem. The new criterion is simpler than the criterion that we presented earlier. A determinental criterion is also presented.  2003 Elsevier Science (USA). All rights reserved