Sampling and Birkhoff regular problems

• Autores: Mahmoud H. Annaby, S. A Buterin, G. Freiling
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 87, Nº 3, 2009, págs. 289-310
• Idioma: inglés
• DOI: 10.1017/s144678870900024x
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• Resumen

  • We establish new sampling representations for linear integral transforms associated with arbitrary general Birkhoff regular boundary value problems. The new approach is developed in connection with the analytical properties of Green�s function, and does not require the root functions to be a basis or complete. Unlike most of the known sampling expansions associated with eigenvalue problems, the results obtained are, generally speaking, of Hermite interpolation type.