#### Title

On the recovery of a differential equation from its spectral functions

#### Document Type

Article

#### Rights

This item is available under a Creative Commons License for non-commercial use only

#### Disciplines

1.1 MATHMATICS

#### Abstract

We consider an inverse spectral problem associated with differential equations of the form y Ž . qx y Ž. Ž . 0 1.1 on 0, . with the boundary condition y Ž. Ž . Ž. Ž . . Ž . 0 cos y 0 sin 0 for some 0, . 1.2 1 We assume throughout that q is a real-valued member of L 0, ., loc defined and finite on 0, . Ž. . We further suppose that q is such that 1.1 is in the limit point case at infinity. Let H and Ž . respectively denote the self-adjoint operator and the spectral function associated with 1.1 Ž . and 1.2 . It will be helpful below also to consider the equation 1.1 on the Ž. Ž. interval X, . for X 0 with the boundary condition y XŽ . Ž. Ž . Ž. Ž . cos y

#### Recommended Citation

Gilbert, D.J. & Harris, B.J. (2001). On the recovery of a differential equation from its spectral functions. *Journal of Mathematical Analysis and Applications*, vol. 262, no. 1, pg. 355-364.
doi:10.1006/jmaa.2001.7585

#### DOI

https://doi.org/10.1006/jmaa.2001.7585