Nonisospectral Flows on Semi-infinite Jacobi Matrices

Isospectral flows on a class of finite-dimensional Jacobi matrices

We present a new matrix-valued isospectral ordinary differential equation that asymptotically block-diagonalizes n × n zero-diagonal Jacobi matrices employed as its initial condition. This o.d.e. features a right-hand side with a nested commutator of matrices, and structurally resembles the double-bracket o.d.e. studied by R.W. Brockett in 1991. We prove that its solutions converge asymptotical...

M-functions and Inverse Spectral Analysis for Finite and Semi-infinite Jacobi Matrices

We study inverse spectral analysis for finite and semi-infinite Jacobi matrices H. Our results include a new proof of the central result of the inverse theory (that the spectral measure determines H). We prove an extension of Hochstadt’s theorem (who proved the result in the case n = N) that n eigenvalues of an N ×N Jacobi matrix, H, can replace the first n matrix elements in determining H uniq...

The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The Limit-Circle Case∗†‡

We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditions for two real sequences to be the spectra of two different self-adjoint extensions of a Jacobi operator in the limit circle case. ∗Mathematics Subject Classification(2000): 47B36, 49N45,...

The Two - Spectra Inverse Problem for Semi - Infinite Jacobi Matrices in The Limit - Circle Case ∗ † ‡ Luis

We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditions for two real sequences to be the spectra of two different self-adjoint extensions of a Jacobi operator in the limit circle case. Mathematics Subject Classification(2000): 47B36, 49N45, ...

Seminar on Jacobi Matrices