Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems

Resumo

In this paper, we study the relation between the well-posedness of the inverse problem of the recovering the source in an abstract differential equation and the basis property of a certain class of function systems in a Hilbert space. As a consequence, based on the results concerning the well-posedness of inverse problems, we obtain the Riesz basis property and—under certain additional conditions—the Bari basis property of such systems.