Description of invariant subspaces of multiple differentiation operators
type: Item
instance of: scholarly article
title: Description of invariant subspaces of multiple differentiation operators
zbMATH Open document ID: 0829.47006
DOI: 10.1007/BF01212841
author: A. Komarov
published in: Mathematical Notes
publication date: 1994-11-16T00:00:00Z
review text: \(H\) denotes the space of entire functions of one complex variable endowed with the topology of uniform convergence on compact subsets of the complex plane. The author considers \(W\) a closed \(D^n\)-invariant subspace, where \(D^n\) denotes a multiple differentiation operator. He uses a result of \textit{S. G. Merzlyakow} [Mat. Zametki 33, No. 5, 701-713 (1983; Zbl 0541.47006)], to expand \(W\) in the topological direct sum \(W= W_1+ W_2\), where \(W_1\) is the closed span of a certain set of functions \(A_1\). The main result is as follows. There exists a sequence of functions \((f_s)\), such that each function in this sequence is a linear combination of functions in \(A_1\), and such that any function \(f\) in \(W\) has a unique representation of the form \[ f(z)= \sum_{s=1}^\infty c_s f_s (z)+ (Qf) (z), \qquad z\in \mathbb{C}. \] \(Q\) is here the projection of \(W\) on \(W_2\) and the coefficients \(c_s\) are in a space topologically isomorphic to \(W_1\).
Mathematics Subject Classification ID: 47A15
zbMATH DE Number: 687486
zbMATH Keywords: differentiation operator
zbMATH Keywords: space of entire functions of one complex variable
zbMATH Keywords: topology of uniform convergence on compact subsets
reviewed by: V. Matache
MaRDI profile type: Publication
cites work: Théorie générale des fonctions moyenne-périodiques
cites work: Q3704481
cites work: Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals.
cites work: Q3796192
cites work: A new look at interpolation theory for entire functions of one variable
full work available at URL: https://doi.org/10.1007/bf01212841
OpenAlex ID: W1971290292
description: scientific article; zbMATH DE number 687486