کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4672877 1346597 2012 33 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Boundary behavior of analytic functions of two variables via generalized models
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Boundary behavior of analytic functions of two variables via generalized models
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Indagationes Mathematicae - Volume 23, Issue 4, December 2012, Pages 995–1027
نویسندگان
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