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Supersets of wavelet sets |
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| รหัสดีโอไอ | |
| Title | Supersets of wavelet sets |
| Creator | Chokchai Viriyapong |
| Contributor | Songkiat Sumetkijakan |
| Publisher | Chulalongkorn University |
| Publication Year | 2551 |
| Keyword | Wavelets (Mathematics), Set functions |
| Abstract | In this thesis, we consider a two-basic set which is defined as a set whose both integral translations and dyadic dilations cover R and that intersects itself at most twice translationally and dilationally. We obtain some necessary conditions and some sufficient conditions for a two-basic set S to contain a wavelet set. The main results, which are in terms of the relationship between two explicitly constructed subsets A and B of S and two subsets T2 and D2 of S intersecting itself exactly twice translationally and dilationally respectively, are that (1) if A∪B ⊈ T2 ∩D2 then S does not contain a wavelet set; and that (2) if A∪B ⊆ T2∩D2 then every wavelet subset of S must be a subset of S\(A∪B) and if S\(A ∪ B) satisfies a “weak” condition then there exists a wavelet subset of S \ (A ∪ B). |
| URL Website | cuir.car.chula.ac.th |
