Abstract
We study the relationship between the well-posedness of the inverse problem of finding the source and the basis property for a class of systems of functions in a Hilbert space. By way of corollary, we derive the Riesz basis property (and, under certain additional conditions, the Bari basis property) of such systems from known results on the well-posedness of inverse problems.
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Original Russian Text © A.B. Kostin, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 2, pp. 246–256.
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Kostin, A.B. Basis property of a system of functions related to the inverse problem of finding the source. Diff Equat 44, 256–266 (2008). https://doi.org/10.1134/S0012266108020134
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DOI: https://doi.org/10.1134/S0012266108020134