On Weyl-Titchmarsh theory for singular finite difference Hamiltonian systems

[1]  F. Gesztesy,et al.  Trace formulas and Borg-type theorems for matrix-valued Jacobi and Dirac finite difference operators , 2004, math/0408074.

[2]  Matthias Lesch,et al.  On the deficiency indices and self-adjointness of symmetric Hamiltonian systems , 2003 .

[3]  F. Gesztesy,et al.  On Povzner–Wienholtz-type self-adjointness results for matrix-valued Sturm–Liouville operators , 2002, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[4]  L. Sakhnovich.  Basic Facts on Weyl – Titchmarsh Theory , 2022 .

[5]  Andrei Osipov.  On some issues related to the moment problem for the band matrices with operator elements , 2002 .

[6]  Alexander Sakhnovich,et al.  Dirac type and canonical systems: spectral and Weyl–Titchmarsh matrix functions, direct and inverse problems , 2002 .

[7]  A. G. Kostyuchenko,et al.  Complete Indefiniteness Tests for Jacobi Matrices with Matrix Entries , 2001 .

[8]  F. Gesztesy,et al.  Weyl-Titchmarsh M-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators , 2001, math/0102040.

[9]  A. S. Osipov.  Some Properties of Resolvent Sets of Second-Order Difference Operators with Matrix Coefficients , 2000 .

[10]  Rafael Obaya,et al.  Ergodic properties and Weyl M-functions for random linear Hamiltonian systems , 2000, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[11]  Antonio J. Durán,et al.  N-EXTREMAL MATRICES OF MEASURES FOR AN INDETERMINATE MATRIX MOMENT PROBLEM , 2000 .

[12]  F. Gesztesy,et al.  Uniqueness Results for Matrix-Valued Schr\"odinger, Jacobi, and Dirac-Type Operators , 2000, math/0004120.

[13]  B. Simon,et al.  On Local Borg–Marchenko Uniqueness Results , 1999, math/9910089.

[14]  M. Malamud,et al.  The Inverse Spectral Problem for First Order Systems on the Half Line , 1998, math/9805033.

[15]  G. Teschl.  Jacobi Operators and Completely Integrable Nonlinear Lattices , 1999 .

[16]  H. Holden,et al.  Borg-Type Theorems for Matrix-Valued Schrödinger Operators , 1999, math/9905143.

[17]  Steve Clark,et al.  Weyl-titchmarsh M -function Asymptotics for Matrix-valued Schr¨odinger Operators , 2022 .

[18]  Lev A. Sakhnovich,et al.  Spectral Theory of Canonical Differential Systems. Method of Operator Identities , 1999 .

[19]  P. López-Rodríguez.  Riesz's Theorem for Orthogonal Matrix Polynomials , 1999 .

[20]  A. G. Kostyuchenko,et al.  Generalized Jacobi matrices and deficiency numbers of ordinary differential operators with polynomial coefficients , 1999 .

[21]  A. G. Kostyuchenko,et al.  Three-term recurrence relations with matrix coefficients. The completely indefinite case , 1998 .

[22]  H. Holden,et al.  Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies , 1997, solv-int/9705019.

[23]  F. Gesztesy,et al.  On Matrix–Valued Herglotz Functions , 1997, funct-an/9712004.

[24]  Barry Simon,et al.  m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices , 1997 .

[25]  Lev A. Sakhnovich,et al.  Interpolation Theory and Its Applications , 1997 .

[26]  F. Gesztesy,et al.  An Addendum to Krein's Formula , 1997, funct-an/9711003.

[27]  A. Osipov.  Integration of non-abelian langmuir type lattices by the inverse spectral problem method , 1997 .

[28]  B. Simon,et al.  Multiparticle Quantum Scattering with Applications to Nuclear Atomic and Molecular Physics , 1997 .

[29]  H. Holden,et al.  ON TRACE FORMULAS FOR SCHRODINGER-TYPE OPERATORS , 1997 .

[30]  G. Teschl,et al.  On isospectral sets of Jacobi operators , 1996 .

[31]  G. Teschl,et al.  Commutation Methods for Jacobi Operators , 1996 .

[32]  Antonio J. Durán,et al.  ORTHOGONAL MATRIX POLYNOMIALS: ZEROS AND BLUMENTHAL'S THEOREM , 1996 .

[33]  Israel Gohberg,et al.  Inverse spectral problems for difference operators with rational scattering matrix function , 1994 .

[34]  W. Assche,et al.  Orthogonal matrix polynomials and higher-order recurrence relations , 1993, math/9310220.

[35]  B. Simon,et al.  On the Toda and Kac-van Moerbeke Systems , 2022 .

[36]  Albert Schneider,et al.  On the Titchmarsh‐Weyl Coefficients for Singular S‐Hermitian Systems II , 1993 .

[37]  A. Sakhnovich,et al.  SPECTRAL FUNCTIONS OF A CANONICAL SYSTEM OF ORDER $ 2n$ , 1992 .

[38]  M. Gekhtman,et al.  Inverse problem of the spectral analysis and non-Abelian chains of nonlinear equations , 1990 .

[39]  Allan M. Krall,et al.  M (λ) theory for singular Hamiltonian systems with two singular points , 1989 .

[40]  B. Simon,et al.  Stochastic Schrödinger operators and Jacobi matrices on the strip , 1988 .

[41]  F. Atkinson.  On the order of magnitude of Titchmarsh-Weyl functions , 1988 .

[42]  M. Shmoish,et al.  Integration of some chains of nonlinear difference equations by the method of the inverse spectral problem , 1986 .

[43]  J. K. Shaw,et al.  On Boundary Value Problems for Hamiltonian Systems with Two Singular Points , 1984 .

[44]  A. Aptekarev,et al.  The Scattering Problem for a Discrete Sturm-Liouville Operator , 1984 .

[45]  J. K. Shaw,et al.  Hamiltonian systems of limit point or limit circle type with both endpoints singular , 1983 .

[46]  J. K. Shaw,et al.  The Asymptotic Form of the Titchmarsh‐Weyl Coefficient for Dirac Systems , 1983 .

[47]  J. K. Shaw,et al.  Parameterization of the M(λ) function for a Hamiltonian system of limit circle type , 1983, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[48]  Jeffrey S. Geronimo,et al.  Scattering theory and matrix orthogonal polynomials on the real line , 1982 .

[49]  J. K. Shaw,et al.  ON THE SPECTRUM OF A SINGULAR HAMILTONIAN SYSTEM , 1982 .

[50]  J. K. Shaw,et al.  On Titchmarsh-Weyl M(λ)-functions for linear Hamiltonian systems , 1981 .

[51]  Morikazu Toda,et al.  Theory Of Nonlinear Lattices , 1981 .

[52]  Erich Müller-Pfeiffer,et al.  Spectral theory of ordinary differential operators , 1981 .

[53]  W. N. Everitt,et al.  On the asymptotic form of the Titchmarsh-Weyl m-coefficient† , 1978 .

[54]  S. A. Orlov,et al.  NESTED MATRIX DISKS ANALYTICALLY DEPENDING PARAMETER, AND THEOREMS ON THE INVARIANCE RADII OF LIMITING DISKS , 1976 .

[55]  Masahisa Fukushima,et al.  A spectral representation on ordinary linear difference equation with operator‐valued coefficients of the second order , 1976 .

[56]  V. I. Kogan,et al.  1.—On Square-integrable Solutions of Symmetric Systems of Differential Equations of Arbitrary Order. , 1976, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[57]  R. Carey.  A unitary invariant for pairs of self-adjoint operators. , 1976 .

[58]  E. Coddington,et al.  Spectral theory of ordinary differential operators , 1975 .

[59]  W. N. Everitt.  Integrable-Square, Analytic Solutions of Odd-Order, Formally Symmetric, Ordinary Differential Equations , 1972 .

[60]  W. N. Everitt.  On a Property of the M -Coefficient of a Secondorder Linear Differential Equation , 1972 .

[61]  W. N. Everitt,et al.  VII.—On the Spectrum of Ordinary Second Order Differential Operators. , 1969, Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences.

[62]  R. Bolstein,et al.  Expansions in eigenfunctions of selfadjoint operators , 1968 .

[63]  W. N. Everitt.  SINGULAR DIFFERENTIAL EQUATIONS II; SOME SELF-ADJOINT EVEN ORDER CASES , 1967 .

[64]  T. Asahi.  Spectral Theory of the Difference Equations , 1966 .

[65]  W. N. Everitt.  Singular differential equations I: The even order case , 1964 .

[66]  F. V. Atkinson,et al.  Discrete and Continuous Boundary Problems , 1964 .

[67]  Nam Parshad Bhatia,et al.  Lectures on ordinary differential equations , 1964 .

[68]  W. N. Everitt.  Fourth order singular differential equations , 1963 .

[69]  V. A. Marchenko,et al.  The Inverse Problem of Scattering Theory , 1963 .

[70]  W. N. Everitt.  Integrable-square solutions of ordinary differential equations (ii) , 1959 .

[71]  N. Aronszajn,et al.  On exponential representations of analytic functions in the upper half-plane with positive imaginary part , 1956 .

[72]  H. Weyl,et al.  Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen , 1910 .