International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 9, Pages 513-523
doi:10.1155/S0161171201010304
Explicit solution for an infinite dimensional generalized inverse eigenvalue problem
School of Mathematics and Statistics, Carleton University, ON, Ottawa K1S 5B6, Canada
Received 28 March 2000; Revised 7 September 2000
Copyright © 2001 Kazem Ghanbari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.