Characterization of tile digit sets with prime determinants
Publication in refereed journal

香港中文大學研究人員

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摘要For an expanding integral s x s matrix A with \det A\ = p, it is well known that if D = {d(0),...,d(p-1)} subset of Z(s) is a complete set of coset representatives of Z(s)/AZ(s), then T(A, D) is a self-affine tile. In this paper we show that if p is a prime, such D actually characterizes the tile digit sets provided that span(D) = R-s. This result is known for s = 1. the one-dimensional case [R. Kenyon, in: Contemp. Math., vol. 135, 1992, pp. 239-264] and the question for s > 1 has been considered by Lagarias and Wang [J. London Math. Soc. 53 (1996) 21-49] under some other conditions. The proof here involves a new setup to study the zeros of the mask m(xi) = p(-1) Sigma(j=0)(p-1) e(2pii(xi,d j)). It can also be generalized to consider the existence of a compactly supported L-1 -solution of the refinement equation (scaling function) with positive coefficients. (C) 2004 Published by Elsevier Inc.
著者He XG, Lau KS
期刊名稱Applied and Computational Harmonic Analysis
出版年份2004
月份5
日期1
卷號16
期次3
出版社ACADEMIC PRESS INC ELSEVIER SCIENCE
頁次159 - 173
國際標準期刊號1063-5203
電子國際標準期刊號1096-603X
語言英式英語
關鍵詞digit set; prime; refinement equation; root of unity; scaling function; self-affine tile; tile digit set
Web of Science 學科類別Mathematics; Mathematics, Applied; MATHEMATICS, APPLIED; Physics; Physics, Mathematical; PHYSICS, MATHEMATICAL

上次更新時間 2021-06-03 於 00:28