Inner functions in polydiscs
نویسندگان
چکیده
منابع مشابه
Busemann Functions and Julia-wolff-carathéodory Theorem for Polydiscs
The classical Julia-Wolff-Carathéodory Theorem is one of the main tools to study the boundary behavior of holomorphic self-maps of the unit disc of C. In this paper we prove a Julia-Wolff-Carathéodory’s type theorem in the case of the polydisc of Cn. The Busemann functions are used to define a class of “generalized horospheres” for the polydisc and to extend the notion of non-tangential limit. ...
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The purpose of this article is to establish Jackson-type inequality in the polydiscs UN of C for holomorphic spaces X, such as Bergman-type spaces, Hardy spaces, polydisc algebra and Lipschitz spaces. Namely, E k(f,X) (−→ 1/k, f,X ) , where E k(f,X) is the deviation of the best approximation of f ∈ X by polynomials of degree at most kj about the jth variable zj with respect to the X-metric and ...
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© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if c...
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The spectrum of the ∂-Neumann Laplacian on a polydisc in C is explicitly computed. The calculation exhibits that the spectrum consists of eigenvalues, some of which, in particular the smallest ones, are of infinite multiplicity.
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An explicit construction characterizing the operator-valued Bergman inner functions is given for a class of vector-valued standard weighted Bergman spaces in the unit disk. These operator-valued Bergman inner functions act as contractive multipliers from the Hardy space into the associated Bergman space, and they have a natural interpretation as transfer functions for a related class of discret...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1967
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1967-11755-5