Authors: Stanković, Radomir 
Astola, Jaakko
Moraga, Claudio
Title: Gibbs Dyadic Differentiation on Groups - Evolution of the Concept
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 10672 LNCS
First page: 229
Last page: 237
Conference: 16th International Conference on Computer Aided Systems Theory, EUROCAST 2017; Las Palmas de Gran Canaria; Spain; 19 February 2017 through 24 February 2017
Issue Date: 1-Jan-2018
Rank: M33
ISBN: 978-3-319-74726-2
ISSN: 0302-9743
DOI: 10.1007/978-3-319-74727-9_27
Differential operators are usually used to determine the rate of change and the direction of change of a signal modeled by a function in some appropriately selected function space. Gibbs derivatives are introduced as operators permitting differentiation of piecewise constant functions. Being initially intended for applications in Walsh dyadic analysis, they are defined as operators having Walsh functions as eigenfunctions. This feature was used in different generalizations and extensions of the concept firstly defined for functions on finite dyadic groups. In this paper, we provide a brief overview of the evolution of this concept into a particlar class of differential operators for functions on various groups.
Publisher: Springer Link

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