A multiple point Nevanlinna-Pick type interpolation problem with both interior and boundary data for Caratheodory matrix-valued functions

作者：Hu Yong-Jian^*; Song Yan-Ping; Chen Gong-Ning

来源：Mathematische Nachrichten, 2011, 284(10): 1304-1328.

DOI：10.1002/mana.200810010

• Caratheodory matrix-valued function
• multiple point Nevanlinna-Pick interpolation problem
• trigonometric matrix moment problem
• block Toeplitz vector
• block Pick matrix
• block Toeplitz matrix

The main theme of this paper is a study of a multiple point Nevanlinna-Pick type interpolation problem with both interior and boundary data for Caratheodory matrix-valued functions. The so-called Toeplitz vector approach is applied to expose intrinsic connections between such an interpolation problem and a certain truncated trigonometric matrix moment problem with specified constraints that the nonnegative matrix-valued measure has no mass distributions at the boundary interpolation nodes. These connections, together with recent results due to Bolotnikov and Dym, enable us to get solvability criteria for both the Nevanlinna-Pick interpolation problem and the matrix moment problem under consideration. On the basis of the developed theory of matrix moments we can derive parameterized descriptions of all the solutions of these two problems in the nondegenerate case.

• 出版日期2011-7
• 单位新疆农业大学; 北京师范大学