Scattering theory and matrix orthogonal polynomials on the real line

K. M. Case and M. Kac, A discrete version of the inverse scattering problem, J. Math. Phy. 14 (1973), 544–603.

J. S. Geronimo and K. M. Case, Scattering theory and polynomials orthogonal on the unit circle, J. Math. Phys. 20 (1979), 299–310.

J. S. Geronimo and K. M. Case, Scattering theory and polynomials orthogonal on the real line, Trans. Amer. Math. Soc. 258 (1980), 467–494.

J. S. Geronimo. A relation between the coefficients in the recurrence formula and the spectral function for orthogonal polynomials, Trans. Amer. Math. Soc. 260 (1980), 65–82.

J. S. Geronimo, An upper bound on the number of eigenvalues of an infinite dimensional Jacobi matrix, Accepted J. Math. Phys.

G. V. Guseinov, The determination of an infinite Jacobi matrix from the scattering data, Soviet Math. Dokl. 17, (1976), 596–600.

H. Dym and A. Iacob, Applications of factorization and Toeplitz operators to inverse problems. Toeplitz memorial conference.

P. G. Nevai, “Orthogonal polynomials.” Memoirs Amer. Math. Soc. 18, 1979.

V. P. Serebrjakov, The inverse problem of scattering theory for difference equations with matrix coefficients. Soviet Math. Dokl. 21, (1980), 148.

F. V. Atkinson, Discrete and Continuous Boundary Problems. Academic Press, New York, 1964.

W. G. Christian, A. G. Law, W. F. Martens, A. L. Mullikin and M. B. Sledd. Solutions of initial-value problems for some infinite chains of harmonic oscillators. J. Math. Phys. 17 (1976), 146.

P. Delsarte, Y. V. Genin, Y. G. Kamp. Orthogonal polynomial matrices on the unit circle. I.E.E.E. Transactions on Circuits and Systems. CAS-25, (1978), 149.

J. S. Geronimo, Matrix orthogonal polynomials on the unit circle. J. Math. Phys, (1981), 1359.

Z. S. Agranovich and V. A. Marchenko, “The Inverse Problem of Scattering Theory,” Gordon and Breach, New York, 1963.

Ju. M. Berezanskii. “Expansions in eigenfunctions of self-adjoint operators,” Trans. Math. Mono. Amer. Math. Soc. 17 (1968).

M. G. Krein. InfiniteJ-matrices and a matrix moment problem, Dokl. Akad. Nauk. SSSR. 69 (1949), 125.

M. Rosenberg, The square-integrability of matrix-valued functions with respect to a non-negative hermitian measure, Duke Math. J. 31 (1964), 291.

K. M. Case, Orthogonal polynomials from the viewpoint of scattering theory, J. Math. Phys. 15 (1974), 2166.

R. G. Newton and R. Jost, The construction of potentials from theS-matrix for systems of differential equations, Il. Nuovo Cimento 1, (1955) 590.