Boundary behavior of analytic functions of two variables via generalized models
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- Professor Jim Agler
- Professor Nicholas Young
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| Author(s) | | Agler J, Tully-Doyle R, Young NJ |
| Publication type | | Article |
| Journal | | Indagationes Mathematicae |
| Year | | 2012 |
| Volume | | 23 |
| Issue | | 4 |
| Pages | | 995-1027 |
| ISSN (print) | | 0019-3577 |
| ISSN (electronic) | | 1872-6100 |
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| Full text is available for this publication: |
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| We describe a generalization of the notion of a Hilbert space model of a function in the Schur class of the bidisc. This generalization is well adapted to the investigation of boundary behavior at a mild singularity of the function on the 2-torus. We prove the existence of a generalized model with certain properties corresponding to such a singularity and use this result to solve two function-theoretic problems. The first of these is to characterise the directional derivatives of a function in the Schur class at a singular point on the torus for which the Carath\'eodory condition holds. The second is to obtain a representation theorem for functions in the two-variable Pick class analogous to the refined Nevanlinna representation of functions in the one-variable Pick class. |
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| Publisher | | Elsevier BV |
| URL | | http://dx.doi.org/10.1016/j.indag.2012.07.003 |
| DOI | | 10.1016/j.indag.2012.07.003 |
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