On the space \(G(\lambda)\) of entire functions
type: Item
instance of: scholarly article
title: On the space \(G(\lambda)\) of entire functions
zbMATH Open document ID: 0551.46016
author: R. P. Agarwal
author: Rajiv K. Srivastava
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1983-01-01T00:00:00Z
review text: \textit{D. Somasundaram} in Ind. J. Pure Appl. Math. 5, 921-932 (1974; Zbl 0247.46024), has studied a Hilbert space \(G(\lambda)\) of entire Talyor series defined by: \(G(\lambda)=\{f(z)=\sum^{\infty}_{n=0}a_ nz^ n;\sum^{\infty}_{n=0}\lambda_ n| a_ n|^ 2<\infty \},\) where \(\{\lambda_ n\}\) is a sequence of positive reals such that \(\{\lambda^{1/n}\}\uparrow \infty\) as \(m\to \infty\). A pointwise multiplier from \(G(\lambda)\) to \(G(\mu)\) is a function h such that \(hf\in G(\mu)\), (\(\forall)\) \(f\in G(\lambda)\). The authors studied the multipliers bewteeen \(G(\lambda)\) and various other Frechet spaces. They have improved two results about these multipliers contained in Somasundaram's work. In the second part of the work, the authors have defined a weighted Hadamard multiplication on \(G(\lambda)\) and they proved that \(G(\lambda)\) has a Banach algebra structure with this multiplication and they have characterized the topological zero divisors and the quasi-invertible elements.
reviewed by: A.Donescu
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 46H05
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 3877788
zbMATH Keywords: Hilbert space of entire Taylor series
zbMATH Keywords: pointwise multiplier
zbMATH Keywords: weighted Hadamard multiplication
zbMATH Keywords: Banach algebra structure
zbMATH Keywords: topological zero divisors
zbMATH Keywords: quasi-invertible elements
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3877788