The Initial Functions in a Cascade Algorithm
نویسنده
چکیده
In this paper we shall study the initial functions in a cascade algorithm in a Sobolev space. By investigating the mutual relations among the initial functions in a cascade algorithm, we are able to study in a relatively unified approach several questions related to cascade algorithms and subdivision schemes in a Sobolev space W k p (Rs) (1 6 p 6∞, k ∈ N∪{0}) such as convergence, error estimate and convergence rate of cascade algorithms and subdivision schemes in a Sobolev space with a general isotropic dilation matrix. The approach in this paper can also be used to study vector cascade algorithms and vector subdivision schemes with a dilation matrix in a multidimensional space.
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