A Constrained Nevanlinna-Pick Interpolation Problem for Matrix-valued Functions

作者：Ball Joseph A^*; Bolotnikov Vladimir; ter Horst Sanne

来源：Indiana University Mathematics Journal, 2010, 59(1): 15-51.

DOI：10.1512/iumj.2010.59.3776

• Nevanlinna-Pick interpolation
• matrix-valued functions
• reproducing kernel
• linear matrix inequalities

Recent results of Davidson-Paulsen-Raghupathi-Singh give necessary and sufficient conditions for the existence of a solution to the Nevanlinna-Pick interpolation problem on the unit disk with the additional restriction that the interpolanr should have the value of its derivative at the origin equal to zero. This concrete mild generalization of the classical problem is prototypical of a number of other generalized Nevanlinna-Pick interpolation problems which have appeared in the literature (for example, on a finitely-connected planar domain or on the polydisk). We extend the results of Davidson-Paulsen-Raghupathi-Singh to the setting where the interpolant is allowed to be matrix-valued and elaborate further on the analogy with the theory of Nevanlinna-Pick interpolation on a finitely-connected planar domain.

• 出版日期2010
• 单位美国弗吉尼亚理工大学(Virginia Tech)