Abstract
We present an accurate investigation of the algebraic conditions that the symbols of a univariate, binary, Hermite subdivision scheme have to fulfil in order to reproduce polynomials. These conditions are sufficient for the scheme to satisfy the so called spectral condition. The latter requires the existence of particular polynomial eigenvalues of the stationary counterpart of the Hermite scheme. In accordance with the known Hermite schemes, we here consider the case of a Hermite scheme dealing with function values, first and second derivatives. Several examples of application of the proposed algebraic conditions are given in both the primal and the dual situation. • We study reproduction of polynomials of Hermite subdivision schemes. • All our methods are purely algebraic and work directly on the subdivision symbols. • These conditions are sufficient for the scheme to satisfy the so called spectral condition. • Examples of application of the proposed conditions are given and new schemes are derived.
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