Extremal problems in the Fock space
type: Item
instance of: scholarly article
title: Extremal problems in the Fock space
zbMATH Open document ID: 1201.30028
DOI: 10.1007/BF03321762
author: Catherine Bénéteau
author: Brent J. Carswell
author: Sherwin Kouchekian
published in: Computational Methods and Function Theory
publication date: 2010-06-17T00:00:00Z
review text: This well-written paper investigates some extremal problems in the Fock space. The Fock space, \(F^2\), consists of those entire functions \(f\) for which \(\|f\|_{2}^2=\int_{\mathbb C}|f(z)|^2 e^{-|z|^2}\,dA(z)<\infty, \) where \(dA(z)=\frac{1}{\pi}dxdy\) is the normalized area measure. After an informative introduction, the authors prove some fundamental results (cf. Section 2) pertaining to the order and type of an entire function in the Fock space. In Section 3, they study the zeros of the extremal functions for zero-based subspaces. In addition, the authors solve a Carathéodory-type extremal problem for functions in \(F^2\) (Section 4).
reviewed by: George Csordas
Mathematics Subject Classification ID: 30D15
Mathematics Subject Classification ID: 30E05
zbMATH DE Number: 5723307
zbMATH Keywords: Fock spaces
zbMATH Keywords: entire functions
zbMATH Keywords: extremal problems
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03321762
OpenAlex ID: W2041872910
description: scientific article; zbMATH DE number 5723307