On an integral transform associated with the regular Dirac operator

Authors: García A.G.; Hernández-Medina M.A.

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Volume 131, Number 6, 14 December 2001 , pp. 1357-1370(14)

Publisher: Royal Society of Edinburgh

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Abstract:

In this paper we deal with a linear integral transform, defined on a vectorial L2-space, whose kernel arises from a one-dimensional system of Dirac operators. Unlike the regular Sturm-Liouville transform, which is associated with a regular Sturm-Liouville problem, the range of this transform is a whole Paley-Wiener space. As a consequence, some results for the Paley-Wiener space are derived; in particular, the sampling formula associated with a regular Dirac operator. Finally, we obtain an inversion formula by means of a continuous measure for suitable Sobolev spaces in the initial L2-space.

Document Type: Research article

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