Minimum w-entropy interpolants for matricial Carathéodory functions and maximum determinant completions of associated block Pick matrix |
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Authors: | Gong-Ning Chen |
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Institution: | School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People’s Republic of China |
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Abstract: | The so-called modified block Toeplitz vector approach is used to connect a class of particular solutions Gw for w∈D of a nondegenerate interpolation problem of the Nevanlinna-Pick type with a class of particular solutions Fw of a certain matricial Carathéodory coefficient problem in a transparent way. This will suggest a simple approach to the minimum w-entropy interpolants and the maximum determinant completions of the associated block Pick matrix within the framework of that Nevanlinna-Pick type interpolation problem by using the known assertions corresponding to Fw. It turns out that Gw(w∈D) is exactly or provides us with the unique solution to these two extremal problems in a manner. |
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Keywords: | 30E05 47A56 |
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