NDLI: On multiplicative and additive differences

Content Provider	Springer Nature Link
Author	Székelyhidi, László Ebanks, Bruce
Copyright Year	2005
Abstract	This paper is about the characterization of those functions which can be expressed as a sum of a generalized polynomial and a generalized logarithmic polynomial. The simplest case of generalized polynomials and generalized logarithmic polynomials of the first degree is to characterize those functions which are sums of affine and logarithmic functions. This problem is solved in [4]. The main result of this article is the following characterization theorem: A function $f\,:\,\mathbb{R}_ + \to \mathbb{R}$ is the sum of a generalized polynomial of degree at most n and of a generalized logarithmic polynomial of degree at most m if and only if all of its m-th multiplicative differences are generalized polynomials of degree at most n.
Ending Page	113
Page Count	17
Starting Page	97
File Format	PDF
ISSN	00019054
e-ISSN	14208903
Journal	Aequationes mathematicae
Issue Number	1
Volume Number	69
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2005-01-01
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	multiplicative differences additive differences Functional equations Analysis General Combinatorics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics

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On multiplicative and additive differences