Effective noncommutative Nevanlinna-Pick interpolation in the row ball, and applications
We provide an effective single-matrix criterion, in terms of what we call the elementary Pick matrix, for the solvability of the noncommutative Nevanlinna-Pick interpolation problem in the row ball, and provide some applications. In particular we show that the so-called “column-row property” fails f...
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| Veröffentlicht in: | Journal of mathematical analysis and applications 2020-12, Vol.492 (2), p.124457, Article 124457 |
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| container_title | Journal of mathematical analysis and applications |
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| creator | Augat, Meric Jury, Michael T. Pascoe, James Eldred |
| description | We provide an effective single-matrix criterion, in terms of what we call the elementary Pick matrix, for the solvability of the noncommutative Nevanlinna-Pick interpolation problem in the row ball, and provide some applications. In particular we show that the so-called “column-row property” fails for the free semigroup algebras, in stark contrast to the analogous commutative case. Additional applications of the elementary Pick matrix include a local dilation theorem for matrix row contractions and interpolating sequences in the noncommutative setting. Finally we present some numerical results related to the failure of the column-row property. |
| doi_str_mv | 10.1016/j.jmaa.2020.124457 |
| format | Article |
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| subjects | Free semigroup algebra Mathematics Mathematics, Applied Nevanlinna-Pick interpolation Noncommutative function theory Physical Sciences Science & Technology |
| title | Effective noncommutative Nevanlinna-Pick interpolation in the row ball, and applications |
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