Abstract
We construct a self-adjoint operator associated with the following given set of eigenvalues: {an+c}n≤−1∪{an+b}n≥0. This problem arises in sampling theory and deals with the construction of an interpolating basis associated with a given set of sampling points, the so-called two sided cardinal series. In order to solve this inverse spectral problem we shall need to extend the Gelfand–Levitan theory to operators close to the Laguerre differential operator.
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