Autonomous functions
type: Item
instance of: scholarly article
title: Autonomous functions
zbMATH Open document ID: 0674.34004
DOI: 10.1016/0022-0396(88)90143-X
author: Lee A. Rubel
author: Michael F. Singer
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: A function y(x) is said to be differentially algebraic if it satisfies a nontrivial algebraic differential equation \(P(x,y)\equiv P(x,y(x),y'(x),...,y^{(n)}(x))=0\) where P is a polynomial in its \(n+1\) variables with complex coefficients. A function f(x) is said to be autonomous if it is differentially algebraic and every translate \(f_ s=f(t-s)\) satisfies every algebraic differential equation which is satisfied by f. The paper deals with the following: 1. Equivalent definitions of an autonomous function; 2. Sums and products of autonomous functions; 3. Composition with autonomous entire functions; 4. Finite sums of periodic functions; 5. Open problems; 6. A short and accessible proof of the Kochin-Ostrowski theorem.
Mathematics Subject Classification ID: 34A99
zbMATH DE Number: 4103468
zbMATH Keywords: algebraic differential equation
zbMATH Keywords: autonomous function
zbMATH Keywords: Kochin-Ostrowski theorem
MaRDI profile type: Publication
Wikidata QID: Q56812651
cites work: On Integral and Meromorphic Functions
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cites work: Über die faktorisierbaren Lösungen gewöhnlicher Differentialgleichungen
full work available at URL: 0022-0396(88)90143-x
OpenAlex ID: W4210651468
description: scientific article; zbMATH DE number 4103468