Orthogonal two-direction multiscaling functions

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  • Department of Mathematics, Shantou University, Shantou 515063, China

Published date: 05 Dec 2006

Abstract

The concept of a two-direction multiscaling functions is introduced. We investigate the existence of solutions of the two-direction matrix refinable equation imagewhere r × r matrices {P+k } and {P-k } are called the positive-direction and negative-direction masks, respectively. Necessary and sufficient conditions that the above two-direction matrix refinable equation has a compactly supported distributional solution are established. The definition of orthogonal two-direction multiscaling function is presented, and the orthogonality criteria for two-direction multiscaling function is established. An algorithm for constructing a class of two-direction multiscaling functions is obtained. In addition, the relation of both orthogonal two-direction multiscaling function and orthogonal multiscaling function is discussed. Finally, construction examples are given.

Cite this article

XIE Changzhen, XIE Changzhen, YANG Shouzhi, YANG Shouzhi . Orthogonal two-direction multiscaling functions[J]. Frontiers of Mathematics in China, 2006 , 1(4) : 604 -611 . DOI: 10.1007/s11464-006-0031-9

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