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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| Format: | Conference or Workshop Item |
| Language: | English English |
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AIP Publishing LLC
2017
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| 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 |
| _version_ | 1825823872131268608 |
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| 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. |
| collection | UMP |
| 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. |
| first_indexed | 2024-03-06T12:17:34Z |
| format | Conference or Workshop Item |
| id | UMPir18437 |
| institution | Universiti Malaysia Pahang |
| language | English English |
| last_indexed | 2024-03-06T12:17:34Z |
| publishDate | 2017 |
| publisher | AIP Publishing LLC |
| record_format | dspace |
| spelling | UMPir184372018-01-31T00:25:45Z 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 (Published) http://dx.doi.org/10.1063/1.4972150 DOI: 10.1063/1.4972150 |
| 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 |
| title | 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_short | A New Structure for Scaling Functions System with Dyadic Intervals |
| title_sort | new structure for scaling functions system with dyadic intervals |
| topic | Q Science (General) |
| 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 |
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