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A New Structure for Scaling Functions System with Dyadic Intervals

A scaling functions system is a series of subspaces {Vj}j∈Z that are embedded and spanned by a group of scaling basis functions {ϕj,k}. To fully grasp how to construct this system using a unique function ϕ(x) ∈ L2(Ij,k) when {Ij,k} is the Dyadic intervals set, its structure is studied. The Dyadic in...

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Main Authors: Shamsah, Raghad S., Ahmedov, Anvarjon A., Hishamuddin, Zainuddin, Kilicman, Adem, Fudziah, Ismail
Format: Conference or Workshop Item
Language:English
English
Published: AIP Publishing LLC 2017
Subjects:
Q Science (General)
Online Access:http://umpir.ump.edu.my/id/eprint/18437/1/A%20new%20structure%20for%20scaling%20functions%20system%20with%20Dyadic%20intervals.pdf
http://umpir.ump.edu.my/id/eprint/18437/2/A%20new%20structure%20for%20scaling%20functions%20system%20with%20Dyadic%20intervals%201.pdf
http://umpir.ump.edu.my/id/eprint/18437/
http://dx.doi.org/10.1063/1.4972150
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spelling my.ump.umpir.184372018-01-31T00:25:45Z http://umpir.ump.edu.my/id/eprint/18437/ A New Structure for Scaling Functions System with Dyadic Intervals Shamsah, Raghad S. Ahmedov, Anvarjon A. Hishamuddin, Zainuddin Kilicman, Adem Fudziah, Ismail Q Science (General) A scaling functions system is a series of subspaces {Vj}j∈Z that are embedded and spanned by a group of scaling basis functions {ϕj,k}. To fully grasp how to construct this system using a unique function ϕ(x) ∈ L2(Ij,k) when {Ij,k} is the Dyadic intervals set, its structure is studied. The Dyadic intervals structure show us that is no any intersection appear between their sub intervals at the different scaling and shifting values. This property introduced a new way to prove the orthonormality of this system by using the supported intervals of the step functions. A new scaling relation ܲPk called the scaling filter is defined on Dyadic intervals, is used to characterize this system. This filter allows for analyzing L2(Ij,k) and other spaces by multi-resolution analysis, as well as it provides some of the requisite conditions. To explain the structure of this system, the clarity examples are given. AIP Publishing LLC 2017 Conference or Workshop Item PeerReviewed application/pdf en http://umpir.ump.edu.my/id/eprint/18437/1/A%20new%20structure%20for%20scaling%20functions%20system%20with%20Dyadic%20intervals.pdf application/pdf en http://umpir.ump.edu.my/id/eprint/18437/2/A%20new%20structure%20for%20scaling%20functions%20system%20with%20Dyadic%20intervals%201.pdf Shamsah, Raghad S. and Ahmedov, Anvarjon A. and Hishamuddin, Zainuddin and Kilicman, Adem and Fudziah, Ismail (2017) A New Structure for Scaling Functions System with Dyadic Intervals. In: 2nd International Conference and Workshop on Mathematical Analysis 2016 (ICWOMA2016), 2–4 August 2016 , Langkawi, Malaysia. pp. 1-8., 1795 (1). ISSN 0094-243X ISBN 978-0-7354-1461-7 http://dx.doi.org/10.1063/1.4972150 DOI: 10.1063/1.4972150
institution Universiti Malaysia Pahang
building UMP Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Pahang
content_source UMP Institutional Repository
url_provider http://umpir.ump.edu.my/
language English
English
topic Q Science (General)
spellingShingle Q Science (General)
Shamsah, Raghad S.
Ahmedov, Anvarjon A.
Hishamuddin, Zainuddin
Kilicman, Adem
Fudziah, Ismail
A New Structure for Scaling Functions System with Dyadic Intervals
description A scaling functions system is a series of subspaces {Vj}j∈Z that are embedded and spanned by a group of scaling basis functions {ϕj,k}. To fully grasp how to construct this system using a unique function ϕ(x) ∈ L2(Ij,k) when {Ij,k} is the Dyadic intervals set, its structure is studied. The Dyadic intervals structure show us that is no any intersection appear between their sub intervals at the different scaling and shifting values. This property introduced a new way to prove the orthonormality of this system by using the supported intervals of the step functions. A new scaling relation ܲPk called the scaling filter is defined on Dyadic intervals, is used to characterize this system. This filter allows for analyzing L2(Ij,k) and other spaces by multi-resolution analysis, as well as it provides some of the requisite conditions. To explain the structure of this system, the clarity examples are given.
format Conference or Workshop Item
author Shamsah, Raghad S.
Ahmedov, Anvarjon A.
Hishamuddin, Zainuddin
Kilicman, Adem
Fudziah, Ismail
author_facet Shamsah, Raghad S.
Ahmedov, Anvarjon A.
Hishamuddin, Zainuddin
Kilicman, Adem
Fudziah, Ismail
author_sort Shamsah, Raghad S.
title A New Structure for Scaling Functions System with Dyadic Intervals
title_short A New Structure for Scaling Functions System with Dyadic Intervals
title_full A New Structure for Scaling Functions System with Dyadic Intervals
title_fullStr A New Structure for Scaling Functions System with Dyadic Intervals
title_full_unstemmed A New Structure for Scaling Functions System with Dyadic Intervals
title_sort new structure for scaling functions system with dyadic intervals
publisher AIP Publishing LLC
publishDate 2017
url http://umpir.ump.edu.my/id/eprint/18437/1/A%20new%20structure%20for%20scaling%20functions%20system%20with%20Dyadic%20intervals.pdf
http://umpir.ump.edu.my/id/eprint/18437/2/A%20new%20structure%20for%20scaling%20functions%20system%20with%20Dyadic%20intervals%201.pdf
http://umpir.ump.edu.my/id/eprint/18437/
http://dx.doi.org/10.1063/1.4972150
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score 13.211869

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