2016, Graduate Studies in Mathematics, ISBN 9781470419134, Volume 168., 326

Book

2.
Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates

Memoirs of the American Mathematical Society, ISSN 0065-9266, 11/2011, Volume 214, Issue 1007, pp. 1 - 84

Let X be a metric space with doubling measure, and L be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on L-2(X). In this article we...

Molecule | BMO | Space of homogeneous type | Davies-Gaffney condition | Non-negative self-adjoint operator | Schrödinger operators | Atom | Hardy space | FUNCTIONAL-CALCULUS | RIESZ TRANSFORMS | REVERSE HOLDER INEQUALITY | HEAT KERNEL BOUNDS | non-negative self-adjoint operator | MATHEMATICS | space of homogeneous type | SEMIGROUP KERNELS | 2ND-ORDER ELLIPTIC-OPERATORS | R-N | MAXIMAL FUNCTIONS | Schrodinger operators | molecule | atom | SCHRODINGER-OPERATORS | RIEMANNIAN-MANIFOLDS

Molecule | BMO | Space of homogeneous type | Davies-Gaffney condition | Non-negative self-adjoint operator | Schrödinger operators | Atom | Hardy space | FUNCTIONAL-CALCULUS | RIESZ TRANSFORMS | REVERSE HOLDER INEQUALITY | HEAT KERNEL BOUNDS | non-negative self-adjoint operator | MATHEMATICS | space of homogeneous type | SEMIGROUP KERNELS | 2ND-ORDER ELLIPTIC-OPERATORS | R-N | MAXIMAL FUNCTIONS | Schrodinger operators | molecule | atom | SCHRODINGER-OPERATORS | RIEMANNIAN-MANIFOLDS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 04/2018, Volume 169, pp. 1 - 37

We study multiple eigenvalues of a magnetic Aharonov–Bohm operator with Dirichlet boundary conditions in a planar domain. In particular, we study the structure...

Aharonov–Bohm potential | Multiple eigenvalues | Magnetic Schrödinger operators | MATHEMATICS | MATHEMATICS, APPLIED | VARYING POLES | Magnetic Schrodinger operators | HAMILTONIANS | Aharonov-Bohm potential | NODAL SETS | SCHRODINGER-OPERATORS | BOUNDARY-BEHAVIOR | Numerical analysis

Aharonov–Bohm potential | Multiple eigenvalues | Magnetic Schrödinger operators | MATHEMATICS | MATHEMATICS, APPLIED | VARYING POLES | Magnetic Schrodinger operators | HAMILTONIANS | Aharonov-Bohm potential | NODAL SETS | SCHRODINGER-OPERATORS | BOUNDARY-BEHAVIOR | Numerical analysis

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 05/2018, Volume 274, Issue 9, pp. 2499 - 2531

We consider the Schrödinger operator with constant magnetic field defined on the half-plane with a Dirichlet boundary condition, H0, and a decaying electric...

Boundary conditions | Spectral shift function | Magnetic Schrödinger operators | Pseudodifferential calculus | MATHEMATICS | Magnetic Schrodinger operators | TOEPLITZ-OPERATORS | PAULI OPERATORS | SYMBOLS | EIGENVALUE ASYMPTOTICS | SCHRODINGER-OPERATORS | DIRAC | Mathematics | Spectral Theory

Boundary conditions | Spectral shift function | Magnetic Schrödinger operators | Pseudodifferential calculus | MATHEMATICS | Magnetic Schrodinger operators | TOEPLITZ-OPERATORS | PAULI OPERATORS | SYMBOLS | EIGENVALUE ASYMPTOTICS | SCHRODINGER-OPERATORS | DIRAC | Mathematics | Spectral Theory

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 472, Issue 2, pp. 1420 - 1429

We show that the spectral measure of discrete Schrödinger operators (Hu)(n)=u(n+1)+u(n−1)+V(n)u(n) does not have singular continuous component if the potential...

Singular continuous spectrum | Weyl function | Discrete Schrödinger operator | MATHEMATICS | Discrete Schrodinger operator | MATHEMATICS, APPLIED | MATRICES

Singular continuous spectrum | Weyl function | Discrete Schrödinger operator | MATHEMATICS | Discrete Schrodinger operator | MATHEMATICS, APPLIED | MATRICES

Journal Article

2011, Contemporary mathematics, ISBN 9780821868980, Volume 552, viii, 224

Book

Bulletin des sciences mathématiques, ISSN 0007-4497, 2019, Volume 152, pp. 93 - 149

This paper is devoted to giving definitions of Besov spaces on an arbitrary open set Ω of Rn via the spectral theorem for the Schrödinger operator with the...

Schrödinger operators | Potential of Kato class | Besov spaces | DISTRIBUTIONS | MATHEMATICS, APPLIED | LIPSCHITZ | Schrodinger operators | DECOMPOSITION | WAVE-EQUATION | SCHRODINGER-OPERATORS

Schrödinger operators | Potential of Kato class | Besov spaces | DISTRIBUTIONS | MATHEMATICS, APPLIED | LIPSCHITZ | Schrodinger operators | DECOMPOSITION | WAVE-EQUATION | SCHRODINGER-OPERATORS

Journal Article

Journal of functional analysis, ISSN 0022-1236, 2019, Volume 277, Issue 9, pp. 3187 - 3235

We construct the continuous Anderson hamiltonian on (−L,L)d driven by a white noise and endowed with either Dirichlet or periodic boundary conditions. Our...

White noise | Regularity structures | Anderson hamiltonian | Schrödinger operator | MATHEMATICS | Schrodinger operator | THEOREM

White noise | Regularity structures | Anderson hamiltonian | Schrödinger operator | MATHEMATICS | Schrodinger operator | THEOREM

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2018, Volume 51, Issue 26, p. 265202

We provide sufficient conditions to have at least one N-particle bound state below the essential spectrum of a large class of N-particle discrete Schrodinger...

cluster operators | essential spectrum | short-range pair potentials | dispersion functions | Schrödinger operator | bound states | HVZ theorem | DISCRETE SPECTRUM ASYMPTOTICS | PARTICLES | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | EIGENVALUES | SYSTEMS | Schrodinger operator | HAMILTONIANS | SCHRODINGER-OPERATORS

cluster operators | essential spectrum | short-range pair potentials | dispersion functions | Schrödinger operator | bound states | HVZ theorem | DISCRETE SPECTRUM ASYMPTOTICS | PARTICLES | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | EIGENVALUES | SYSTEMS | Schrodinger operator | HAMILTONIANS | SCHRODINGER-OPERATORS

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 02/2020, Volume 134, pp. 72 - 121

Given any Borel function V:Ω→[0,+∞] on a smooth bounded domain Ω⊂RN, we establish that the strong maximum principle for the Schrödinger operator −Δ+V in Ω...

Green's function | Strong maximum principle | Schrödinger operator | Singular potential | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | KATOS INEQUALITY | Schrodinger operator | ELLIPTIC-EQUATIONS | POTENTIALS | SCHRODINGER-OPERATORS

Green's function | Strong maximum principle | Schrödinger operator | Singular potential | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | KATOS INEQUALITY | Schrodinger operator | ELLIPTIC-EQUATIONS | POTENTIALS | SCHRODINGER-OPERATORS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2018, Volume 464, Issue 1, pp. 616 - 661

We consider the Schrödinger operator on a combinatorial graph consisting of a finite graph and a finite number of discrete half-lines, all jointed together,...

Resolvent expansion | Generalized eigenfunction | Resonance | Combinatorial graph | Schrödinger operator | Threshold | MATHEMATICS | MATHEMATICS, APPLIED | Schrodinger operator

Resolvent expansion | Generalized eigenfunction | Resonance | Combinatorial graph | Schrödinger operator | Threshold | MATHEMATICS | MATHEMATICS, APPLIED | Schrodinger operator

Journal Article

Chaos, solitons and fractals, ISSN 0960-0779, 2019, Volume 120, pp. 83 - 94

We consider a class of Lévy-type processes with unbounded coefficients, arising as Doob h-transforms of Feynman-Kac type representations of non-local...

Non-local Schrödinger operators | Stochastic differential equations | Hausdorff dimension | Ground states | Jump processes | Feynman-Kac semigroups | Sample path properties | FALL-OFF | PHYSICS, MULTIDISCIPLINARY | SPECTRAL PROPERTIES | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Non-local Schrodinger operators | PACKING DIMENSION | SCHRODINGER-OPERATORS | LEVY | RANGE

Non-local Schrödinger operators | Stochastic differential equations | Hausdorff dimension | Ground states | Jump processes | Feynman-Kac semigroups | Sample path properties | FALL-OFF | PHYSICS, MULTIDISCIPLINARY | SPECTRAL PROPERTIES | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Non-local Schrodinger operators | PACKING DIMENSION | SCHRODINGER-OPERATORS | LEVY | RANGE

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 04/2020, Volume 278, Issue 7, p. 108415

Let T be the generator of a C0-semigroup e−Tt which is of trace class for all t>0 (a Gibbs semigroup). Let A be another closed operator, T-bounded with T-bound...

Perturbation of Gibbs semigroups | Non-selfadjoint Schrödinger operators | Dyson-Phillips expansion | MATHEMATICS | Non-selfadjoint Schrodinger operators | OPERATORS

Perturbation of Gibbs semigroups | Non-selfadjoint Schrödinger operators | Dyson-Phillips expansion | MATHEMATICS | Non-selfadjoint Schrodinger operators | OPERATORS

Journal Article

Geometric and functional analysis, ISSN 1420-8970, 2011, Volume 21, Issue 5, pp. 1001 - 1019

We develop a new KAM scheme that applies to SL(2, $${{\mathbb R}}$$ ) cocycles with one frequency, irrespective of any Diophantine condition on the base...

Quasiperiodic cocycles | Analysis | reducibility | 37E20 | ergodic Schrödinger operators | Mathematics | 37J40 | MATHEMATICS | EXPONENTS | MATRICES | SINGULAR CONTINUOUS-SPECTRUM | ergodic Schrodinger operators | PERIODIC SCHRODINGER-OPERATORS | ABSOLUTELY CONTINUOUS-SPECTRUM | Probability

Quasiperiodic cocycles | Analysis | reducibility | 37E20 | ergodic Schrödinger operators | Mathematics | 37J40 | MATHEMATICS | EXPONENTS | MATRICES | SINGULAR CONTINUOUS-SPECTRUM | ergodic Schrodinger operators | PERIODIC SCHRODINGER-OPERATORS | ABSOLUTELY CONTINUOUS-SPECTRUM | Probability

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2016, Volume 49, Issue 16, p. 165302

We analyze two-dimensional Schrodinger operators with the potential vertical bar xy vertical bar(p)-lambda(x(2)+ y(2))(p/(p+2)) where p >= 1 and lambda >= 0...

eigenvalue estimates | spectral transition | Schrödinger operator | PHYSICS, MULTIDISCIPLINARY | QUANTUM | Schrodinger operator | MODEL | PHYSICS, MATHEMATICAL

eigenvalue estimates | spectral transition | Schrödinger operator | PHYSICS, MULTIDISCIPLINARY | QUANTUM | Schrodinger operator | MODEL | PHYSICS, MATHEMATICAL

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2010, Volume 249, Issue 2, pp. 253 - 304

Spectral properties of 1-D Schrödinger operators H X , α : = − d 2 d x 2 + ∑ x n ∈ X α n δ ( x − x n ) with local point interactions on a discrete set X = { x...

Self-adjointness | Discreteness | Local point interaction | Schrödinger operator | Lower semiboundedness | SPECTRAL THEORY | MATHEMATICS | Schrodinger operator | HAMILTONIANS | QUANTUM-MECHANICS

Self-adjointness | Discreteness | Local point interaction | Schrödinger operator | Lower semiboundedness | SPECTRAL THEORY | MATHEMATICS | Schrodinger operator | HAMILTONIANS | QUANTUM-MECHANICS

Journal Article

The Annals of probability, ISSN 0091-1798, 2009, Volume 37, Issue 3, pp. 815 - 852

We consider N x N Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of...

Integers | Flux density | Spectral theory | Expected values | Eigenvalues | Eigenvectors | Matrices | Random variables | Semicircles | Greens function | Density of states | Random Schrödinger operator | Localization | Semicircle law | Extended states | Wigner random matrix | localization | extended states | STATISTICS & PROBABILITY | random Schrodinger operator | density of states | random Schrödinger operator | 15A52 | 82B44

Integers | Flux density | Spectral theory | Expected values | Eigenvalues | Eigenvectors | Matrices | Random variables | Semicircles | Greens function | Density of states | Random Schrödinger operator | Localization | Semicircle law | Extended states | Wigner random matrix | localization | extended states | STATISTICS & PROBABILITY | random Schrodinger operator | density of states | random Schrödinger operator | 15A52 | 82B44

Journal Article

1996, Applied mathematical sciences, ISBN 0387945016, Volume 113., ix, 337

Book

Journal of the European Mathematical Society, ISSN 1435-9855, 2019, Volume 21, Issue 3, pp. 777 - 795

We establish Anderson localization for quasiperiodic operator families of the form ( (x)psi )(m) = psi (m + 1) + psi (m - 1) + lambda v(x + m alpha)psi(m) for...

Purely point spectrum | Anderson localization | Quasiperiodic Schrödinger operator | MATHEMATICS | MATHIEU OPERATOR | MATHEMATICS, APPLIED | HOLDER CONTINUITY | purely point spectrum | SHIFTS | quasiperiodic Schrodinger operator | CONTINUOUS-SPECTRUM | DENSITY-OF-STATES | LYAPUNOV EXPONENT | SCHRODINGER-OPERATORS

Purely point spectrum | Anderson localization | Quasiperiodic Schrödinger operator | MATHEMATICS | MATHIEU OPERATOR | MATHEMATICS, APPLIED | HOLDER CONTINUITY | purely point spectrum | SHIFTS | quasiperiodic Schrodinger operator | CONTINUOUS-SPECTRUM | DENSITY-OF-STATES | LYAPUNOV EXPONENT | SCHRODINGER-OPERATORS

Journal Article

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