Smoothness of multivariate refinable functions with infinitely supported masks

Authors:
Jianbin Yang;Song Li
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou, 310027, PR China;Department of Mathematics, Zhejiang University, Hangzhou, 310027, PR China
Venue:
Journal of Approximation Theory
Year:
2010

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Abstract

In this paper, we investigate the smoothness of multivariate refinable functions with infinitely supported masks and an isotropic dilation matrix. Using some methods as in [R.Q. Jia, Characterization of smoothness of multivariate refinable functions in Sobolev spaces, Trans. Amer. Math. Soc. 351 (1999) 4089-4112], we characterize the optimal smoothness of multivariate refinable functions with polynomially decaying masks and an isotropic dilation matrix. Our characterizations extend some of the main results of the above mentioned paper with finitely supported masks to the case in which masks are infinitely supported.