A nonlinear dynamical system on the set of Laguerre entire functions
type: Item
instance of: scholarly article
title: A nonlinear dynamical system on the set of Laguerre entire functions
zbMATH Open document ID: 1112.30307
DOI: 10.1016/S0362-546X(01)00098-0
author: Lech Wołowski
author: Yuri Kozitsky
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-01-01T00:00:00Z
review text: It is well-known that the Laguerre entire functions are obtained as uniform limits on compact subsets of \(\mathbb C\) of the sequences of polynomials which have only real nonpositive zeros. In [Complex Variables, Theory Appl. 44, No. 3, 225--244 (2001; Zbl 1037.46022)], the authors considered the set \(L\) of such functions and described it in the framework of locally convex spaces of exponential type entire functions. Among other things, it was proved that the Cauchy problem \[ \begin{cases} \frac{\partial f(t,z)}{\partial t}=\theta\frac{\partial f(t,z)}{\partial z}+z\frac{\partial^2f(t,z)}{\partial z^2},\, t\in\mathbb R^+,\, z\in\mathbb C,\\ f(0,z)=g(z),\, g\in L,\, \theta\geq 0,\end{cases} \] has a unique solution in \(L\), at least for \(t\) small enough. In the present paper, the authors consider a nonlinear modification of this problem and prove new results. This is an essential contribution in the subject.
Mathematics Subject Classification ID: 30G20
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1740571
reviewed by: Themistocles M. Rassias
MaRDI profile type: Publication
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full work available at URL: s0362-546x(01)00098-0
OpenAlex ID: W2096065608
description: scientific article; zbMATH DE number 1740571