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

DOI

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

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