Abstract: In this paper we will first prove that the nontrivial L_p solutions of the vector refinement equation exist if and only if the corresponding subdivision scheme with a suitable initial function converges in L_p without assumption of the stability of the solutions. Then we obtain a characterization of the convergence of the subdivision scheme in terms of the mask. This gives a complete answer to the existence of L_p solutions of the refinement equation and the convergence of the corresponding subdivision schemes.

Key words: Refinement equations, Subdivision schemes, Joint spectral radius

Please provide your name, email address and a comment

Your Name: Affili: E-Mail Address:

Comment (Please comment in English):


Verification Code(click to change a pic):