A Hilbert space approach to bounded analytic interpolation (Q2468344)

The authors develop an approach of Fitzgerald and Horn in bounded analytic interpolation to the case of several complex variables and operator-valued interpolation. In particular, they give a sufficient condition for the Nevanlinna--Pick-type interpolation problem \(v(z_{1,\alpha},z_{2,\beta})=w_{\alpha,\beta}\), where \(z_{1,\alpha}\in D_1\), \(z_{2,\beta}\in D_2\), \(D_i\) are domains in \(\mathbb C^d\), \(v\) is analytic in both variables on \(D_1\times D_2\), to have a solution. The key ingredient in the author's method is the Kolmogorov Factorization Lemma.