Self-Affine Scaling Sets in R2

Xiaoye Fu, Jean-Pierre Gabardo (Autoren)

Buch | Softcover

85 Seiten

2015
American Mathematical Society (Verlag)
978-1-4704-1091-9 (ISBN)

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There are many non-integral self-affine tiles which can yield wavelet basis. In this work, the author gives a complete characterization of all one and two dimensional A-dilation scaling sets K such that K is a self-affine tile satisfying BK=(K d1)(K d2) for some d1,d2?R2, where A is a 2×2 integral expansive matrix with detA=2 and B=At

There exist results on the connection between the theory of wavelets and the theory of integral self-affine tiles and in particular, on the construction of wavelet bases using integral self-affine tiles. However, there are many non-integral self-affine tiles which can also yield wavelet basis. In this work, the author gives a complete characterization of all one and two dimensional A -dilation scaling sets K such that K is a self-affine tile satisfying BK=(K d1)⋃(K d2) for some d1,d2∈R2 , where A is a 2×2 integral expansive matrix with ∣detA∣=2 and B=At

Xiaoye Fu, The Chinese University of Hong Kong, Shatin, Hong Kong. Jean-Pierre Gabardo, McMaster University, Hamilton, ON, Canada.

Introduction
Preliminary results
A sufficient condition for a self-affine tile to be an MRA scaling set
Characterization of the inclusion K⊂BK
Self-affine scaling sets in R2: the case 0∈D
Self-affine scaling sets in R2: the case D={d1,d2}⊂R2
Conclusion
Bibliography

Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	200 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-1091-5 / 1470410915
ISBN-13	978-1-4704-1091-9 / 9781470410919
Zustand	Neuware