In the phase retrieval problem one seeks to recover an unknown function g(t) from the amplitude mod g(k) mod of its Fourier transform. Since phase and amplitude are, in general, independent of each other, it is necessary to make use of other kinds of information which implicitly or explicitly constrain the admissible solutions g(t). In this paper we survey a variety of results explaining circumstances under which g(t) may be uniquely recovered from mod g(k) mod and supplementary information. A number of explicit formulae for the phase are discussed. We pay particular attention to the phase retrieval problem as it arises in certain inverse-scattering applications.

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This paper gives constructive algorithms for the classical inverse Sturm-Liouville problem. It is shown that many of the formulations of this problem are equivalent to solving an overdetermined boundary value problem for a certain hyperbolic operator. Two methods of solving this latter problem are then provided, and numerical examples are presented.

Abstract. This paper gives constructive algorithms for the classical inverse Sturm-Liouville problem. It is shown that many of the formulations of this problem are equivalent to solving an overdetermined boundary value problem for a certain hyperbolic operator. Two methods of solving this latter problem are then provided, and numerical examples are presented.