Self-affine scaling sets in R² / Xiaoye Fu, Jean-Pierre Gabardo.

Format:

Book

Author/Creator:

Fu, Xiaoye, 1979- author.

Gabardo, Jean-Pierre, 1958- author.

Series:

Memoirs of the American Mathematical Society ; Volume 233, Number 1097 (third of 6 numbers)

Memoirs of the American Mathematical Society, 1947-6221 ; Volume 233, Number 1097 (third of 6 numbers)

Language:

English

Subjects (All):

Scaling laws (Statistical physics).

Wavelets (Mathematics).

R (Computer program language).

Physical Description:

1 online resource (85 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2014.

Language Note:

English

Summary:

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

Contents:

Cover

Title page

Chapter 1. Introduction

1.1. Wavelets and Wavelet Sets

1.2. Scaling Sets

1.3. Self-Affine Tiles

1.4. Main Results

Chapter 2. Preliminary Results

Chapter 3. A sufficient condition for a self-affine tile to be an MRA scaling set

Chapter 4. Characterization of the inclusion ⊂

Chapter 5. Self-affine scaling sets in ℝ²: the case 0∈

5.1. The case = ₁

5.2. The case = ₂

5.3. The case = ₃

5.4. The case =- ₃

5.5. The case = ₄

5.6. The case =- ₄

Chapter 6. Self-affine scaling sets in ℝ²: the case ={ ₁, ₂}⊂ℝ²

6.1. The case = ₁

6.2. The case = ₂

6.3. The case = ₃,- ₃, ₄,- ₄

Chapter 7. Conclusion

Bibliography

Index

Back Cover.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-1965-3