Bibliographic Details
| Title: |
More on Carathéodory Theorem for Matrix-Valued Schur Functions. |
| Authors: |
Xuzhou Zhan1 xzzhan@bnu.edu.cn, Wei Wei1 weilovely@bnu.edu.cn, Yongjian Hu1 yongjian@bnu.edu.cn, Gongning Chen1 gnchen@bnu.edu.cn |
| Superior Title: |
Southeast Asian Bulletin of Mathematics. 2022, Vol. 46 Issue 5, p649-680. 32p. |
| Subject Terms: |
*SCHUR functions, *MAXIMAL functions, *NEVANLINNA theory, *INTERPOLATION |
| Abstract: |
In this paper Carath'eodoery theorem for matrix-valued Schur functions and its two basic corollaries, due to Arov, are supplemented with several important results especially, under some conditions, about the uniqueness of the spectral function sup-porting maximal jump of full rank at a given boundary point. An essential step is to derive an effective coupling identity between the jumps of every spectral function and some canonical one at that boundary point. A by-product of this identity is simplified proofs of a number of remarkable properties for canonical spectral functions. These extend the region of their applications. As examples, we elucidate simultaneously corresponding known extremal feature for various matrix moment problems and interpolation problems of the Nevanlinna-Pick type in the completely indeterminate case, and a number of additions to them. [ABSTRACT FROM AUTHOR] |
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| Database: |
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