کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4672877 | 1346597 | 2012 | 33 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Boundary behavior of analytic functions of two variables via generalized models Boundary behavior of analytic functions of two variables via generalized models](/preview/png/4672877.png)
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 characterize the directional derivatives of a function in the Schur class at a singular point on the torus for which the Carathéodory 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.
Journal: Indagationes Mathematicae - Volume 23, Issue 4, December 2012, Pages 995–1027