A generalization of the Beurling--Lax theorem
type: Item
instance of: scholarly article
title: A generalization of the Beurling--Lax theorem
zbMATH Open document ID: 1128.46014
published in: Mathematical Notes
publication date: 2007-05-21T00:00:00Z
review text: The authors obtain conditions for the completeness of the system \(\{G(z)e^{\tau z},\tau\leq 0\}\) in the space \(H^2_\sigma(\mathbb{C}_+)\), \(0< \sigma<+\infty\), of functions analytic in the right-hand half-plane with the norm \[ \|f\|:=\sup_{-\pi/2<\varphi<\pi/2}\left\{\int^{+\infty}_0|f (re^{i\varphi})|^2e^{-2r\sigma|\sin\varphi|}dr \right\}^{1/2}<+ \infty. \]
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 37A15
zbMATH DE Number: 5155459
zbMATH Keywords: Beurling-Lax theorem
zbMATH Keywords: analytic function
zbMATH Keywords: Hardy space
author: B. V. Vynnyts'kyj
author: V. M. Dil'nyj
reviewed by: Bahmann Yousefi
MaRDI profile type: Publication
full work available at URL: s11006-006-0038-2
OpenAlex ID: W2361208789
cites work: Scattering Theory for Automorphic Functions. (AM-87)
cites work: COMPLEX FOURIER--BESSEL TRANSFORMS
cites work: On a theorem of Whipple
cites work: On the problem without initial conditions for a nonlinear degenerating parabolic system
cites work: Some questions of the Nevanlinna theory for the complex half-plane
DOI: 10.1007/S11006-006-0038-2
description: scientific article; zbMATH DE number 5155459