On stable refinable function vectors with arbitrary support

• Autores: Sandra Saliani
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 154, Nº 2, 2008, págs. 105-125
• Idioma: inglés
• DOI: 10.1016/j.jat.2008.03.008
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• Resumen

  • Refinable function vectors with arbitrary support are considered. In particular, necessary conditions for stability are given and a characterization of the symbol associated with a stable refinable function vector in terms of the transfer operator is provided: this is a generalization of Gundy�s theorem to the vector case. The proof adapts the tools provided in [S. Saliani, On stability and orthogonality of refinable functions, Appl. Comput. Harmon. Anal. 21 (2006) 254�261]. Though complications arise from noncommuting matrix products, the fundamental ideas are the same.