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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 Sahib, Ahatjonovich, Anvarjon Ahmedov, Zainuddin, Hishamuddin, Kilicman, Adem, Ismail, Fudziah
Format: Conference or Workshop Item
Language:English
Published: AIP Publishing 2016
Online Access:http://psasir.upm.edu.my/id/eprint/57648/1/A%20new%20structure%20for%20scaling%20functions%20system%20with%20Dyadic%20intervals.pdf
http://psasir.upm.edu.my/id/eprint/57648/
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spelling my.upm.eprints.576482017-10-24T09:06:17Z http://psasir.upm.edu.my/id/eprint/57648/ A new structure for scaling functions system with Dyadic intervals Shamsah, Raghad Sahib Ahatjonovich, Anvarjon Ahmedov Zainuddin, Hishamuddin Kilicman, Adem Ismail, Fudziah 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 2016 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57648/1/A%20new%20structure%20for%20scaling%20functions%20system%20with%20Dyadic%20intervals.pdf Shamsah, Raghad Sahib and Ahatjonovich, Anvarjon Ahmedov and Zainuddin, Hishamuddin and Kilicman, Adem and Ismail, Fudziah (2016) A new structure for scaling functions system with Dyadic intervals. In: 2nd International Conference and Workshop on Mathematical Analysis (ICWOMA 2016), 2-4 Aug. 2016, Langkawi, Malaysia. (pp. 1-8). 10.1063/1.4972150
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
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 Sahib
Ahatjonovich, Anvarjon Ahmedov
Zainuddin, Hishamuddin
Kilicman, Adem
Ismail, Fudziah
spellingShingle Shamsah, Raghad Sahib
Ahatjonovich, Anvarjon Ahmedov
Zainuddin, Hishamuddin
Kilicman, Adem
Ismail, Fudziah
A new structure for scaling functions system with Dyadic intervals
author_facet Shamsah, Raghad Sahib
Ahatjonovich, Anvarjon Ahmedov
Zainuddin, Hishamuddin
Kilicman, Adem
Ismail, Fudziah
author_sort Shamsah, Raghad Sahib
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
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/57648/1/A%20new%20structure%20for%20scaling%20functions%20system%20with%20Dyadic%20intervals.pdf
http://psasir.upm.edu.my/id/eprint/57648/
_version_ 1643836549876416512
score 13.211869

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