On the construction of Jacobi matrices from spectral data

Abstract

The problem of constructing an n by n Jacobi matrix J with prescribed spectrum {λ_i}ⁿ₁, such that the submatrix J(Ï), obtained from J by deleting its Ï^th row and column, also has a prescribed spectrum {ðœ‡_i}^n-1₁ is studied. The cases Ï=1 and Ï=n are well known. For the case 2 â‰¤ Ï â‰¤ n-1 it is shown that the problem has a unique solution under the condition Î»_i < ðœ‡_i < Î»_i+1, i=1, 2, . . . , n-1.