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Gibbs Dyadic Differentiation on Groups - Evolution of the Concept

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Details

Original languageEnglish
Title of host publicationComputer Aided Systems Theory – EUROCAST 2017 - 16th International Conference, Revised Selected Papers
PublisherSpringer Verlag
Pages229-237
Number of pages9
ISBN (Print)9783319747262
DOIs
Publication statusPublished - 2018
Publication typeA4 Article in a conference publication
EventINTERNATIONAL CONFERENCE ON COMPUTER AIDED SYSTEMS THEORY -
Duration: 1 Jan 1900 → …

Publication series

NameLecture Notes in Computer Science
Volume10672
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceINTERNATIONAL CONFERENCE ON COMPUTER AIDED SYSTEMS THEORY
Period1/01/00 → …

Abstract

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.

Publication forum classification

Field of science, Statistics Finland