From Taylor interpolation to Hermite interpolation via duality

• Autores: Marie-Laurence Mazure
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 4, Nº. 1, 2012, págs. 15-45
• Idioma: inglés
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• Resumen

  • The present work concerns W-spaces, that is, spaces which permit Taylor interpolation on a given interval. We introduce the critical length of any given W-space E as the supremum of all positive h ensuring that E permits Hermite interpolation (i.e., E is an Extended Chebyshev space) on any subinterval of length h. The critical length may be equal to 0, but it is always positive if the interval is closed and bounded. Any W-space is allocated to a dual space. When the dual space is a W-space in turn, we can take advantage of its presence to calculate the critical length.

    The notion of critical length was first introduced in [3] for null spaces of linear differential operator with constant coefficients. As a special case, the use of duality gives new insights into the practical expressions to obtain the critical length of such null spaces