A Class of Matrix-valued Schrödinger Operators with Prescribed Finite-band Spectra

[1]  L. Dickey Soliton Equations and Hamiltonian Systems , 2003 .

[2]  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.

[3]  R. Carlson An Inverse Problem for the Matrix Schrödinger Equation , 2002 .

[4]  H. Chern,et al.  Extension of Ambarzumyan's Theorem to General Boundary Conditions , 2001 .

[5]  chaoyu shen Some inverse spectral problems for vectorial Sturm-Liouville equations , 2001 .

[6]  Chao-Liang Shen Some inverse spectral problems for vectorial Sturm-Liouville equations , 2001 .

[7]  R. Carlson Eigenvalue Estimates and Trace Formulas for the Matrix Hill's Equation , 2000 .

[8]  I. Polterovich Heat kernel asymptotics for Laplace type operators and matrix KdV hierarchy , 2000, math/0010057.

[9]  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.

[10]  chaoyu shen Some eigenvalue problems for the vectorial Hill's equation , 2000 .

[11]  F. Gesztesy,et al.  Uniqueness Results for Matrix-Valued Schrodinger, Jacobi, and Dirac-Type Operators , 2000, math/0004120.

[12]  R. Carlson Compactness of Floquet isospectral sets for the matrix Hill's equation , 2000 .

[13]  H. Dym,et al.  J-Inner matrix functions, interpolation and inverse problems for canonical systems, II: The inverse monodromy problem , 2000 .

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

[15]  Chao-Liang Shen Some eigenvalue problems for the vectorial Hill's equation , 2000 .

[16]  H. Dym,et al.  J-inner matrix functions, interpolation and inverse problems for canonical systems, III: More on the inverse monodromy problem , 2000 .

[17]  M. Loss,et al.  A simple proof of a theorem of Laptev and Weidl , 1999, math-ph/9906024.

[18]  R. Carlson Large eigenvalues and trace formulas for matrix Sturm-Liouville problems , 1999 .

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

[20]  Steve Clark,et al.  Weyl–Titchmarsh M‐Function Asymptotics for Matrix‐valued Schrödinger Operators , 1999, math/9905070.

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

[22]  H. Chern On the Construction of Isospectral Vectorial Sturm-Liouville Differential Equations , 1999, math/9902041.

[23]  chaoyu shen,et al.  Two inverse eigenvalue problems for vectorial Sturm-Liouville equations , 1998 .

[24]  D. Alpay,et al.  Inverse problem for Sturm-Liouville operators with rational reflection coefficient , 1998 .

[25]  Peter J. Olver,et al.  Integrable Evolution Equations on Associative Algebras , 1998 .

[26]  D. Hinton,et al.  A Liapunov Inequality for Linear Hamiltonian Systems , 1998 .

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

[28]  H. Dym,et al.  J-inner matrix functions, interpolation and inverse problems for canonical systems, I: Foundations , 1997 .

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

[30]  A. Sakhnovich Iterated Backlund–Darboux Transform for Canonical Systems☆ , 1997 .

[31]  H. Chern,et al.  On the n-dimensional Ambarzumyan's theorem , 1997 .

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

[33]  A. Sakhnovich Canonical systems and transfer matrix-functions , 1997 .

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

[35]  G. Teschl,et al.  The KDV Hierarchy and Associated Trace Formulas , 1996 .

[36]  P. Yuditskii,et al.  Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum , 1995 .

[37]  B. Simon,et al.  HIGHER ORDER TRACE RELATIONS FOR SCHRÖDINGER OPERATORS , 1995 .

[38]  D. Alpay,et al.  Inverse Spectral Problem for Differential Operators with Rational Scattering Matrix Functions , 1995 .

[39]  B. Després The Borg theorem for the vectorial Hill's equation , 1995 .

[40]  V. Papanicolaou Trace formulas and the behavior of large eigenvalues , 1995 .

[41]  I. Gohberg,et al.  Matrix and Operator Valued Functions: The Vladimir Petrovich Potapov Memorial Volume , 1994 .

[42]  L. Sakhnovich Inverse problems for equations systems , 1994 .

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

[44]  R. Lazarov,et al.  Integral Equations and Inverse Problems , 1991 .

[45]  Y. Kato,et al.  Algebraic and Spectral Methods for Nonlinear Wave Equations , 1990 .

[46]  R. Carmona,et al.  Spectral Theory of Random Schrödinger Operators , 1990 .

[47]  加藤 祐輔,et al.  Algebraic and spectral methods for nonlinear wave equations , 1990 .

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

[49]  R. Schimming An explicit expression for the Korteweg-de Vries hierarchy , 1995, solv-int/9710009.

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

[51]  V. Vol'kovich Infinitely divisible distributions in algebras with stochastic convolution , 1988 .

[52]  L. Sakhnovich Evolution of spectral data and nonlinear equations , 1988 .

[53]  V. Marchenko Nonlinear Equations and Operator Algebras , 1987 .

[54]  Russell Johnson m-functions and Floquet exponents for linear differential systems , 1987 .

[55]  B. M. Levitan,et al.  Inverse Sturm-Liouville Problems , 1987 .

[56]  I. M. Gelfand,et al.  On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients , 1987 .

[57]  E. Olmedilla Inverse scattering transform for general matrix Schrodinger operators and the related symplectic structure , 1985 .

[58]  B. Dubrovin,et al.  Matrix finite-zone operators , 1985 .

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

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

[61]  M. G. Krein,et al.  The Basic Propositions of the Theory of λ-Zones of Stability of a Canonical System of Linear Differential Equations with Periodic Coefficients , 1983 .

[62]  M. Kreĭn,et al.  On tests for stable boundedness of solutions of periodic canonical systems , 1983 .

[63]  L. Alonso,et al.  Trace identities in the inverse scattering transform method associated with matrix Schrödinger operators , 1982 .

[64]  B. M. Levitan On the solvability of the Sturm–Liouville inverse problem on the entire line , 1982 .

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

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

[67]  F. Guil,et al.  Infinite-dimensional Hamiltonian systems associated with matrix Schrödinger operators , 1981 .

[68]  Christine Thurlow A generalisation of the inverse spectral theorem of Levitan and Gasymov , 1979, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[69]  Y. Manin Matrix solitons and bundles over curves with singularities , 1978 .

[70]  M. Kreĭn,et al.  The Markov Moment Problem and Extremal Problems , 1977 .

[71]  F. S. Rofe-Beketov,et al.  ON THE CONNECTION BETWEEN SPECTRAL AND OSCILLATION PROPERTIES OF THE STURM-LIOUVILLE MATRIX PROBLEM , 1977 .

[72]  I. Gel'fand,et al.  The resolvent and Hamiltonian systems , 1977 .

[73]  R. D. Driver,et al.  Ordinary and Delay Differential Equations , 1977 .

[74]  Antonio Degasperis,et al.  Nonlinear evolution equations solvable by the inverse spectral transform.— II , 1977 .

[75]  Boris Dubrovin,et al.  Completely integrable Hamiltonian systems associated with matrix operators and Abelian varieties , 1977 .

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

[77]  Antonio Degasperis,et al.  Nonlinear evolution equations solvable by the inverse spectral transform.—I , 1976 .

[78]  Sergei Petrovich Novikov,et al.  NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES , 1976 .

[79]  A. Markus,et al.  Factorization of a weakly hyperbolic bundle , 1976 .

[80]  S P Novikov,et al.  NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES , 1976 .

[81]  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.

[82]  V. Matveev,et al.  Schrödinger operators with finite-gap spectrum and N-soliton solutions of the Korteweg-de Vries equation , 1975 .

[83]  B. Dubrovin Periodic problems for the Korteweg — de Vries equation in the class of finite band potentials , 1975 .

[84]  V. A. I︠A︡kubovich,et al.  Linear differential equations with periodic coefficients , 1975 .

[85]  M. Wadati,et al.  On the Extension of Inverse Scattering Method , 1974 .

[86]  I. M. Glazman Direct methods of qualitative spectral analysis of singular differential operators , 1965 .

[87]  P. Hartman Ordinary Differential Equations , 1965 .

[88]  B. M. Levitan,et al.  Determination of a Differential Equation by Two of its Spectra , 1964 .

[89]  B M Levitan,et al.  DETERMINATION OF A DIFFERENTIAL EQUATION BY TWO OF ITS SPECTRA , 1964 .

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

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

[92]  L. Goddard Linear Differential Operators , 1962, Nature.

[93]  Ernst Wienholtz Halbbeschränkte partielle Differentialoperatoren zweiter Ordnung vom elliptischen Typus , 1958 .

[94]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[95]  R. Newton,et al.  The construction of potentials from theS-matrix for systems of differential equations , 1955 .

[96]  I. Gel'fand,et al.  On the determination of a differential equation from its spectral function , 1955 .