Explicit solution for an infinite dimensional generalized inverse eigenvalue problem

Abstract

We study a generalized inverse eigenvalue problem (GIEP), Ax=λBx, in which A is a semi-infinite Jacobi matrix with positive off-diagonal entries ci>0, and B= diag (b0,b1,…), where bi≠0 for i=0,1,…. We give an explicit solution by establishing an appropriate spectral function with respect to a given set of spectral data.