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A new structure for scaling functions system with Dyadic intervals


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).


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.

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Additional Metadata

Item Type: Conference or Workshop Item (Paper)
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1063/1.4972150
Publisher: AIP Publishing
Keywords: Scaling functions system; Dyadic intervals; Structure
Depositing User: Nabilah Mustapa
Date Deposited: 24 Oct 2017 09:06
Last Modified: 24 Oct 2017 09:06
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1063/1.4972150
URI: http://psasir.upm.edu.my/id/eprint/57648
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