Semi-Orthogonal Parseval Wavelets Frames on Local Fields and Applications in Manufacturing Science

Shi Heng Wang

doi:10.4028/www.scientific.net/AMR.712-715.2464

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Semi-Orthogonal Parseval Wavelets Frames on Local Fields and Applications in Manufacturing Science
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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 712-715Semi-Orthogonal Parseval Wavelets Frames on Local...

Semi-Orthogonal Parseval Wavelets Frames on Local Fields and Applications in Manufacturing Science

Abstract:

Manufacturing science focuses on understanding problems from the perspective of the stakeholders involved and then applying manufacturing science as needed. We investigate semi-orthogonal frame wavelets and Parseval frame wavelets in with a dilation factor. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces. This result is obtained through considering the basicquestion as to when the orthogonal complement of an afffine subspace in another one is still affine subspace.The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure of is also introduced. The construction of a generalized multireso-lution structure of Paley-Wiener subspaces of is investigated.

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Periodical:

Advanced Materials Research (Volumes 712-715)

Pages:

2464-2468

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.712-715.2464

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Online since:

June 2013

Authors:

Shi Heng Wang

Keywords:

Dilation Reducing Sub-Spaces, Local Fields, Semi-Orthogonal Frame Wavelets, Shift-Invariant Subspaces, Sobelev Space, Time-Frequency Analysis

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