Journal of Functional Analysis, ISSN 0022-1236, 06/2015, Volume 268, Issue 12, pp. 3649 - 3679

... of Schrödinger operators with non-negative matrix-valued potentials, i.e., operators acting on ψ∈L2(Rn,Cd) by the formulaHVψ:=−Δψ+Vψ, where the potential V takes values in the set of non-negative Hermitian d...

Discrete spectrum | Schrödinger operators | Matrix-valued potentials | MATHEMATICS | Schrodinger operators | COMPACTNESS

Discrete spectrum | Schrödinger operators | Matrix-valued potentials | MATHEMATICS | Schrodinger operators | COMPACTNESS

Journal Article

Dissertationes Mathematicae, ISSN 0012-3862, 2010, Issue 469, pp. 4 - 58

Journal Article

Boundary Value Problems, ISSN 1687-2770, 12/2011, Volume 2011, Issue 1, pp. 1 - 8

...+1 characteristic functions can determine the potential function of a vectorial Sturm-Liouville operator uniquely...

Ordinary Differential Equations | Inverse spectral problems | Analysis | Sturm-Liouville equation | Approximations and Expansions | Difference and Functional Equations | Mathematics, general | Mathematics | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX-VALUED SCHRODINGER | THEOREMS | INVERSE PROBLEMS | OPERATORS | Differential equations, Linear | Boundary value problems | Usage | Research | Mathematical research

Ordinary Differential Equations | Inverse spectral problems | Analysis | Sturm-Liouville equation | Approximations and Expansions | Difference and Functional Equations | Mathematics, general | Mathematics | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX-VALUED SCHRODINGER | THEOREMS | INVERSE PROBLEMS | OPERATORS | Differential equations, Linear | Boundary value problems | Usage | Research | Mathematical research

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 09/2017, Volume 529, pp. 51 - 88

.... We establish a simple criterion for the potentials to produce discrete spectrum near the low ground energy of the operators...

Asymptotic expansions | Pauli operators | Complex matrix-valued potentials | Discrete spectrum | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | INEQUALITIES | MAGNETIC-FIELDS | NONSELF-ADJOINT PERTURBATIONS | SCHRODINGER-OPERATORS | DIRAC | Magnetic fields | Analysis

Asymptotic expansions | Pauli operators | Complex matrix-valued potentials | Discrete spectrum | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | INEQUALITIES | MAGNETIC-FIELDS | NONSELF-ADJOINT PERTURBATIONS | SCHRODINGER-OPERATORS | DIRAC | Magnetic fields | Analysis

Journal Article

Journal of functional analysis, ISSN 0022-1236, 10/2020, Volume 279, Issue 6, p. 108609

... for A(⋅,⋅) is uniquely solvable for initial conditionsA(⋅,0)=A(⋅)∈[C1([0,∞))]m2×m1, and the corresponding potential coefficient v∈[C1([0,∞))]m1...

Dirac-type systems | Matrix-valued potentials | Inverse problems | SPECTRAL THEORY | MATHEMATICS | POTENTIALS | SCHRODINGER-TYPE OPERATORS

Dirac-type systems | Matrix-valued potentials | Inverse problems | SPECTRAL THEORY | MATHEMATICS | POTENTIALS | SCHRODINGER-TYPE OPERATORS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 11/2015, Volume 56, Issue 11, p. 112702

We establish simple connections between response functions of the dynamical Dirac systems and A-amplitudes and Weyl functions of the spectral Dirac systems....

WEYL FUNCTIONS | MATRIX-VALUED POTENTIALS | NONLINEAR EQUATIONS | IDENTITIES | DOUBLE COMMUTATION METHOD | CANONICAL SYSTEMS | BOUNDARY CONTROL | PHYSICS, MATHEMATICAL | FORMULAS | SCHRODINGER-TYPE OPERATORS | Response functions | Inverse problems

WEYL FUNCTIONS | MATRIX-VALUED POTENTIALS | NONLINEAR EQUATIONS | IDENTITIES | DOUBLE COMMUTATION METHOD | CANONICAL SYSTEMS | BOUNDARY CONTROL | PHYSICS, MATHEMATICAL | FORMULAS | SCHRODINGER-TYPE OPERATORS | Response functions | Inverse problems

Journal Article

7.
Full Text
Borg's Periodicity Theorems for First-Order Self-Adjoint Systems with Complex Potentials

Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 08/2017, Volume 60, Issue 3, pp. 615 - 633

A self-adjoint first-order system with Hermitian π-periodic potential Q(z), integrable on compact sets, is considered...

Secondary 34L40 | 34B05 | 2010 Mathematics subject classification: Primary 34A55 | JACOBI | MATHEMATICS | MATRIX-VALUED SCHRODINGER | spectral theory | HILLS EQUATION | Dirac system | inverse problems | DOUBLE EIGENVALUES | DIRAC-TYPE | OPERATORS | INVERSE SPECTRAL PROBLEMS | Stability | Equivalence | Periodic functions | Matrices (mathematics)

Secondary 34L40 | 34B05 | 2010 Mathematics subject classification: Primary 34A55 | JACOBI | MATHEMATICS | MATRIX-VALUED SCHRODINGER | spectral theory | HILLS EQUATION | Dirac system | inverse problems | DOUBLE EIGENVALUES | DIRAC-TYPE | OPERATORS | INVERSE SPECTRAL PROBLEMS | Stability | Equivalence | Periodic functions | Matrices (mathematics)

Journal Article

Computational Methods in Applied Mathematics, ISSN 1609-4840, 2006, Volume 6, Issue 2, pp. 194 - 220

Journal Article

ASYMPTOTIC ANALYSIS, ISSN 0921-7134, 2009, Volume 65, Issue 3-4, pp. 147 - 174

.... We derive resolvent estimates for semi-classical Schrodinger operator with matrix-valued potential under a geometric condition of the same type on the crossing set and we analyze examples...

semi-classical Schrodinger equation | SCHRODINGER OPERATOR | EIGENVALUES | MATHEMATICS, APPLIED | eigenvalue crossing | Wigner measure | SEMICLASSICAL ANALYSIS | matrix-valued potential | ABSENCE | normal form | RESONANCES | EQUATION

semi-classical Schrodinger equation | SCHRODINGER OPERATOR | EIGENVALUES | MATHEMATICS, APPLIED | eigenvalue crossing | Wigner measure | SEMICLASSICAL ANALYSIS | matrix-valued potential | ABSENCE | normal form | RESONANCES | EQUATION

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 05/2010, Volume 92, Issue 2, pp. 125 - 141

A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically...

Matrix-valued Schrödinger operator | Cwikel-Lieb-Rozenblum inequality | Supersymmetric matrix models | matrix-valued Schrodinger operator | NUMBER | VALUED POTENTIALS | BOUND-STATES | supersymmetric matrix models | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS

Matrix-valued Schrödinger operator | Cwikel-Lieb-Rozenblum inequality | Supersymmetric matrix models | matrix-valued Schrodinger operator | NUMBER | VALUED POTENTIALS | BOUND-STATES | supersymmetric matrix models | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS

Journal Article

DISSERTATIONES MATHEMATICAE, ISSN 0012-3862, 2010, Issue 469, pp. 5 - 5

The Complex Absorbing Potential (CAP) method is widely used to compute resonances in Quantum Chemistry, both for scalar valued and matrix valued Hamiltonians...

eigenvalues | STATES | LINEAR ELASTICITY | MATRIX SCHRODINGER-OPERATORS | ARBITRARY BODY | nonselfadjoint operators | QUANTUM SCATTERING | MATHEMATICS | TRANSMISSION | propagation of singularities | RESONANCE ENERGIES | scattering | LOWER BOUNDS | matrix valued pseudodifferential operators | DISCRETE VARIABLE REPRESENTATION | SHAPE RESONANCES | perturbations

eigenvalues | STATES | LINEAR ELASTICITY | MATRIX SCHRODINGER-OPERATORS | ARBITRARY BODY | nonselfadjoint operators | QUANTUM SCATTERING | MATHEMATICS | TRANSMISSION | propagation of singularities | RESONANCE ENERGIES | scattering | LOWER BOUNDS | matrix valued pseudodifferential operators | DISCRETE VARIABLE REPRESENTATION | SHAPE RESONANCES | perturbations

Journal Article

St. Petersburg Mathematical Journal, ISSN 1061-0022, 06/2006, Volume 17, Issue 3, pp. 409 - 433

A generalized two-dimensional periodic Dirac operator is considered, with L^{\infty}-matrix-valued coefficients of the first-order derivatives and with complex matrix-valued potential...

Absolutely continuous spectrum | Matrix-valued potential | Generalized periodic Dirac operator

Absolutely continuous spectrum | Matrix-valued potential | Generalized periodic Dirac operator

Journal Article

Journal of Statistical Software, ISSN 1548-7660, 01/2015, Volume 63, Issue 8, pp. 1 - 25

Modeling of and inference on multivariate data that have been measured in space, such as temperature and pressure, are challenging tasks in environmental...

Bivariate Matérn model | Matrix-valued covariance function | Multivariate geostatistics | Multivariate random field | R, Vector-valued field | Linear model of coregionalization

Bivariate Matérn model | Matrix-valued covariance function | Multivariate geostatistics | Multivariate random field | R, Vector-valued field | Linear model of coregionalization

Journal Article

Journal of computational methods in applied mathematics, ISSN 1609-4840, 2006, Volume 6, Issue 2, pp. 194 - 220

The structured tensor-product approximation of multidimensional nonlocal operators by a two-level rank-(r1, . . . , rd) decomposition of related higher-order...

structured matrices | multidimensional integral operators | matrix-valued functions | Kronecker products | Newton potential | higher-order tensors

structured matrices | multidimensional integral operators | matrix-valued functions | Kronecker products | Newton potential | higher-order tensors

Journal Article

15.
Full Text
Convergence of the empirical spectral distribution of gaussian matrix-valued processes

Electronic Journal of Probability, ISSN 1083-6489, 2019, Volume 24

For a given normalized Gaussian symmetric matrix-valued process Y-(n), we consider the process of its eigenvalues {(lambda((n))(1) (t), . . . , lambda((n))(n)...

Skorokhod integral | Free probability | Gaussian matrix-valued processes | Measure valued process | STATISTICS & PROBABILITY | measure valued process | PARTICLES | free probability

Skorokhod integral | Free probability | Gaussian matrix-valued processes | Measure valued process | STATISTICS & PROBABILITY | measure valued process | PARTICLES | free probability

Journal Article

Electronic Journal of Probability, ISSN 1083-6489, 2015, Volume 20, pp. 1 - 29

.... This leads us to develop new results of potential theoretic nature concerning the space of real square matrices...

Positive determinant matrix | Matrix-valued process | Muckenhoupt weight | Wishart process | Bessel process | Reflecting boundary condition | positive determinant matrix | STATISTICS & PROBABILITY | EXTENSION | reflecting boundary condition | Mathematics - Probability

Positive determinant matrix | Matrix-valued process | Muckenhoupt weight | Wishart process | Bessel process | Reflecting boundary condition | positive determinant matrix | STATISTICS & PROBABILITY | EXTENSION | reflecting boundary condition | Mathematics - Probability

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 11/2017, Volume 169, Issue 3, pp. 547 - 594

In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe...

Physical Chemistry | Hitting times | Theoretical, Mathematical and Computational Physics | Quantum random walks | Markov chains | Matrix-valued measures | Quantum Physics | Completely positive map | Physics | Statistical Physics and Dynamical Systems | POLYNOMIALS | MATRIX | PHYSICS, MATHEMATICAL

Physical Chemistry | Hitting times | Theoretical, Mathematical and Computational Physics | Quantum random walks | Markov chains | Matrix-valued measures | Quantum Physics | Completely positive map | Physics | Statistical Physics and Dynamical Systems | POLYNOMIALS | MATRIX | PHYSICS, MATHEMATICAL

Journal Article

Dissertation

Journal of Functional Analysis, ISSN 0022-1236, 2004, Volume 214, Issue 2, pp. 312 - 385

The theory of the direct and bitangential inverse input impedance problem is used to solve the direct and bitangential inverse spectral problem. The analysis...

Canonical systems | Reproducing kernel Hilbert spaces | de Branges spaces | The inverse spectral problem | J-inner matrix valued functions | De Branges spaces | INTERPOLATION | MATHEMATICS | the inverse spectral problem | canonical systems | INNER MATRIX FUNCTIONS | reproducing kernel Hilbert spaces

Canonical systems | Reproducing kernel Hilbert spaces | de Branges spaces | The inverse spectral problem | J-inner matrix valued functions | De Branges spaces | INTERPOLATION | MATHEMATICS | the inverse spectral problem | canonical systems | INNER MATRIX FUNCTIONS | reproducing kernel Hilbert spaces

Journal Article

20.
矩陣值勢能上的sofic測度

... equilibrium measures that correspond to the matrix-valued potential on a sofic shift space. With the construction, the analysis of dimension spectrum is then available...

平衡測度 | matrix-valued potential | equilibrium measure | sofic shift space | 矩陣值勢能 | sofic measure | sofic shift 空間 | sofic 測度 | 維度的譜分析 | dimension spectrum

平衡測度 | matrix-valued potential | equilibrium measure | sofic shift space | 矩陣值勢能 | sofic measure | sofic shift 空間 | sofic 測度 | 維度的譜分析 | dimension spectrum

Dissertation

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