Please use this identifier to cite or link to this item:
|Title:||On the regularity of matrix refinable functions||Authors:||Jiang, Q.||Keywords:||Matrix refinable function
|Issue Date:||Sep-1998||Citation:||Jiang, Q. (1998-09). On the regularity of matrix refinable functions. SIAM Journal on Mathematical Analysis 29 (5) : 1157-1176. ScholarBank@NUS Repository.||Abstract:||It is shown that the transition operator Tp associated with the matrix refinement mask P(ω) = 2-d∑α∈[0, N]dPαexp(-iαω) is equivalent to the matrix (2-dA2i-j)i,j with Aj = ∑κ∈[0, N]dPκ-j⊗Pκ and Pκ-j⊗Pκ denoting the Kronecker product of matrices Pκ-j, Pκ. Some spectral properties of Tp are studied and a complete characterization of the matrix refinable functions in the Sobolev space Wn(Rd) for nonnegative integers n is provided. The Sobolev regularity estimate of the matrix refinable function is given in terms of the spectral radius of a restricted transition operator. These estimates are analyzed in some examples.||Source Title:||SIAM Journal on Mathematical Analysis||URI:||http://scholarbank.nus.edu.sg/handle/10635/103832||ISSN:||00361410|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Apr 11, 2021
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.