Journal of mathematical physics, ISSN 1089-7658, 2014, Volume 55, Issue 8, p. 083520

.... We show that the essential spectrum coincides with the spectrum of a planar tube provided that the second fundamental form of the manifold vanishes at infinity and the transport of the cross-section...

NONNEGATIVE RICCI CURVATURE | LAPLACIAN | BOUND-STATES | DISCRETE SPECTRUM | WAVE-GUIDES | TUBES | PHYSICS, MATHEMATICAL | COMPLETE RIEMANNIAN-MANIFOLDS | Dirichlet problem | Riemann manifold | Euclidean geometry | Euclidean space | CROSS SECTIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EUCLIDEAN SPACE | NANOSTRUCTURES | MATHEMATICAL MANIFOLDS | SPECTRA

NONNEGATIVE RICCI CURVATURE | LAPLACIAN | BOUND-STATES | DISCRETE SPECTRUM | WAVE-GUIDES | TUBES | PHYSICS, MATHEMATICAL | COMPLETE RIEMANNIAN-MANIFOLDS | Dirichlet problem | Riemann manifold | Euclidean geometry | Euclidean space | CROSS SECTIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EUCLIDEAN SPACE | NANOSTRUCTURES | MATHEMATICAL MANIFOLDS | SPECTRA

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2017, Volume 446, Issue 2, pp. 1863 - 1881

.... We give a criterion for the essential spectrum of the Laplacian on the perturbed graph to include that on the unperturbed graph...

Perturbation theory | Infinite graph | Discrete Laplacian | Essential spectrum | Pendant | Random graph | MATHEMATICS | MATHEMATICS, APPLIED | LATTICES | SCHRODINGER-OPERATORS

Perturbation theory | Infinite graph | Discrete Laplacian | Essential spectrum | Pendant | Random graph | MATHEMATICS | MATHEMATICS, APPLIED | LATTICES | SCHRODINGER-OPERATORS

Journal Article

Lobachevskii Journal of Mathematics, ISSN 1995-0802, 5/2017, Volume 38, Issue 3, pp. 530 - 541

.... We proved the essential spectra of the four-electron systems in the quintet state is a single segment, and four-electron anti-bound states or four-electron bound states is absent...

essential spectra | Probability Theory and Stochastic Processes | Hubbard model | bound states | Mathematics | Four-electron systems | anti-bound states | Geometry | Algebra | Analysis | discrete spectrum | Mathematics, general | Mathematical Logic and Foundations

essential spectra | Probability Theory and Stochastic Processes | Hubbard model | bound states | Mathematics | Four-electron systems | anti-bound states | Geometry | Algebra | Analysis | discrete spectrum | Mathematics, general | Mathematical Logic and Foundations

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 1/2015, Volume 25, Issue 1, pp. 536 - 563

... on a family of related warped product spaces. We apply these results to study the essential spectrum of the drifting Laplacian on M.

58J50 | Mathematics | Drifting Laplacian | Heat kernel | Abstract Harmonic Analysis | Harnack inequality | Fourier Analysis | Essential spectrum | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | 58E30 | Differential Geometry | Dynamical Systems and Ergodic Theory | UNIFORMLY ELLIPTIC-OPERATORS | SCHRODINGER OPERATOR | SPACES | Heat kernel | LAPLACIAN | MATHEMATICS | EIGENVALUES | CURVATURE | EMERY-RICCI TENSOR | RIEMANNIAN-MANIFOLDS

58J50 | Mathematics | Drifting Laplacian | Heat kernel | Abstract Harmonic Analysis | Harnack inequality | Fourier Analysis | Essential spectrum | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | 58E30 | Differential Geometry | Dynamical Systems and Ergodic Theory | UNIFORMLY ELLIPTIC-OPERATORS | SCHRODINGER OPERATOR | SPACES | Heat kernel | LAPLACIAN | MATHEMATICS | EIGENVALUES | CURVATURE | EMERY-RICCI TENSOR | RIEMANNIAN-MANIFOLDS

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 10/2015, Volume 25, Issue 4, pp. 2241 - 2261

.... Under these conditions we obtain that the essential spectrum of the Laplace operator contains an interval...

Laplace operator | 53C21 | Mathematics | 47A10 | Riemannian manifold | Abstract Harmonic Analysis | Fourier Analysis | Essential spectrum | Convex and Discrete Geometry | 47A25 | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | LAPLACIAN | MATHEMATICS | CURVATURE | Ants

Laplace operator | 53C21 | Mathematics | 47A10 | Riemannian manifold | Abstract Harmonic Analysis | Fourier Analysis | Essential spectrum | Convex and Discrete Geometry | 47A25 | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | LAPLACIAN | MATHEMATICS | CURVATURE | Ants

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2007, Volume 426, Issue 2, pp. 317 - 324

When A ∈ B ( H ) and B ∈ B ( K ) are given, we denote by M C the operator acting on the infinite dimensional separable Hilbert space H ⊕ K of the form M C = A...

Browder essential approximate point spectrum | Semi-Fredholm operator | Hypercyclic operator | MATHEMATICS | MATHEMATICS, APPLIED | WEYLS THEOREM | hypercyclic operator | semi-Fredholm operator

Browder essential approximate point spectrum | Semi-Fredholm operator | Hypercyclic operator | MATHEMATICS | MATHEMATICS, APPLIED | WEYLS THEOREM | hypercyclic operator | semi-Fredholm operator

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 05/2007, Volume 280, Issue 7, pp. 699 - 716

.... The location of the essential spectrum of the three‐particle discrete Schrödinger...

essential spectrum | eigenvalues | quasi‐momentum | Hamiltonians | lattice | Faddeev type equation | short‐range potentials | quantum mechanical two‐and three‐particle systems | Discrete Schrödinger operators | Discrete schrödinger operators | Quantum mechanical two-and three-particle systems | Essential spectrum | Short-range potentials | Eigenvalues | Quasi-momentum | Lattice | SYSTEM | MATHEMATICS | quasi-momentum | PARTICLES | discrete Schrodinger operators | short-range potentials | quantum mechanical two-and three-particle systems

essential spectrum | eigenvalues | quasi‐momentum | Hamiltonians | lattice | Faddeev type equation | short‐range potentials | quantum mechanical two‐and three‐particle systems | Discrete Schrödinger operators | Discrete schrödinger operators | Quantum mechanical two-and three-particle systems | Essential spectrum | Short-range potentials | Eigenvalues | Quasi-momentum | Lattice | SYSTEM | MATHEMATICS | quasi-momentum | PARTICLES | discrete Schrodinger operators | short-range potentials | quantum mechanical two-and three-particle systems

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 1/2011, Volume 166, Issue 1, pp. 81 - 93

...-dimensional lattice. We identify channel operators and use their spectra to describe the position and structure of the essential spectrum of H...

essential spectrum | channel operator | Theoretical, Mathematical and Computational Physics | Hilbert-Schmidt class | model operator | Faddeev equation | Applications of Mathematics | nonlocal potential | Physics | SCHRODINGER OPERATOR | NONLOCAL POTENTIALS | PARTICLES | PHYSICS, MULTIDISCIPLINARY | DISCRETE SPECTRUM | PHYSICS, MATHEMATICAL

essential spectrum | channel operator | Theoretical, Mathematical and Computational Physics | Hilbert-Schmidt class | model operator | Faddeev equation | Applications of Mathematics | nonlocal potential | Physics | SCHRODINGER OPERATOR | NONLOCAL POTENTIALS | PARTICLES | PHYSICS, MULTIDISCIPLINARY | DISCRETE SPECTRUM | PHYSICS, MATHEMATICAL

Journal Article

Journal of Topology and Analysis, ISSN 1793-5253, 03/2016, Volume 8, Issue 1, pp. 89 - 115

.... In this paper we use the essential circles introduced in [ 19] to define a larger class of covering maps of compact geodesic spaces called "circle covers" that are "closed" with respect to Gromov-Hausdorff convergence and include delta-covers...

discrete homotopy | δ-cover | geodesic space | Gromov-Hausdorff convergence | MATHEMATICS | UNIVERSAL COVERS | FUNDAMENTAL-GROUPS | delta-cover | UNIFORM-SPACES | MANIFOLDS | SPECTRUM

discrete homotopy | δ-cover | geodesic space | Gromov-Hausdorff convergence | MATHEMATICS | UNIVERSAL COVERS | FUNDAMENTAL-GROUPS | delta-cover | UNIFORM-SPACES | MANIFOLDS | SPECTRUM

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 11/2017, Volume 50, Issue 48, p. 485203

.... Depending on whether the operators L and L(V) are positive or not, the spectrum of H-Sm(A) and H(V) exhibits a sharp transition.

discrete spectrum | essential spectrum | spectral transition | homogeneous magnetic field | Smilansky-Solomyak model | IRREVERSIBLE QUANTUM GRAPHS | PHYSICS, MULTIDISCIPLINARY | SPECTRUM | PHYSICS, MATHEMATICAL | DIFFERENTIAL-OPERATORS | FAMILY

discrete spectrum | essential spectrum | spectral transition | homogeneous magnetic field | Smilansky-Solomyak model | IRREVERSIBLE QUANTUM GRAPHS | PHYSICS, MULTIDISCIPLINARY | SPECTRUM | PHYSICS, MATHEMATICAL | DIFFERENTIAL-OPERATORS | FAMILY

Journal Article

Journal of Geometric Analysis, ISSN 1050-6926, 4/2012, Volume 22, Issue 2, pp. 603 - 620

We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers...

Abstract Harmonic Analysis | Fourier Analysis | Essential spectrum | Convex and Discrete Geometry | 58J50 | Global Analysis and Analysis on Manifolds | Mathematics | 57A10 | Differential Geometry | Dynamical Systems and Ergodic Theory | Discrete spectrum | Riemannian submersions | MATHEMATICS | MANIFOLDS | NEGATIVE CURVATURE | Invisibility | Fibers

Abstract Harmonic Analysis | Fourier Analysis | Essential spectrum | Convex and Discrete Geometry | 58J50 | Global Analysis and Analysis on Manifolds | Mathematics | 57A10 | Differential Geometry | Dynamical Systems and Ergodic Theory | Discrete spectrum | Riemannian submersions | MATHEMATICS | MANIFOLDS | NEGATIVE CURVATURE | Invisibility | Fibers

Journal Article

Communications in Mathematics and Statistics, ISSN 2194-6701, 12/2014, Volume 2, Issue 3, pp. 279 - 309

For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing...

Killing | Second-order differential operator (diffusion) | Essential spectrum | 60J60 | Tridiagonal matrix (birth–death process) | 34L05 | Mathematics, general | Mathematics | 60J27 | Statistics, general | Discrete spectrum

Killing | Second-order differential operator (diffusion) | Essential spectrum | 60J60 | Tridiagonal matrix (birth–death process) | 34L05 | Mathematics, general | Mathematics | 60J27 | Statistics, general | Discrete spectrum

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2007, Volume 2008, Issue 1, pp. 1 - 14

.... Moreover, we establish a fine description of the Schechter essential spectrum of a closed densely defined operators...

Mathematics, general | Mathematics | Applications of Mathematics | Analysis | MATHEMATICS | MATHEMATICS, APPLIED | PERTURBATIONS | SPACES | OPERATORS | Banach spaces

Mathematics, general | Mathematics | Applications of Mathematics | Analysis | MATHEMATICS | MATHEMATICS, APPLIED | PERTURBATIONS | SPACES | OPERATORS | Banach spaces

Journal Article

SIAM journal on scientific computing, ISSN 1064-8275, 05/2012, Volume 34, Issue 3, pp. B226 - B246

...) case with large or negative permittivity. We identify very dense line segments in the spectrum as being partly responsible for this behavior and the main reason why a normally efficient deflating preconditioner does not work...

essential spectrum | electromagnetism | transverse electric scattering | regularizer | deflation | singular integral operators | preconditioner | domain integral equation | spectrum of operators | Electromagnetism | Essential spectrum | Preconditioner | Deflation | Regularizer | Spectrum of operators | Domain integral equation | Singular integral operators | Transverse electric scattering | DISCRETE-DIPOLE APPROXIMATION | MATHEMATICS, APPLIED | VOLUME | TE-WAVE SCATTERING | ELECTROMAGNETIC SCATTERING | EQUATION | Operators | Algorithms | Scattering | Eigenvalues | Segments | Acceleration | Preconditioning | Regularization

essential spectrum | electromagnetism | transverse electric scattering | regularizer | deflation | singular integral operators | preconditioner | domain integral equation | spectrum of operators | Electromagnetism | Essential spectrum | Preconditioner | Deflation | Regularizer | Spectrum of operators | Domain integral equation | Singular integral operators | Transverse electric scattering | DISCRETE-DIPOLE APPROXIMATION | MATHEMATICS, APPLIED | VOLUME | TE-WAVE SCATTERING | ELECTROMAGNETIC SCATTERING | EQUATION | Operators | Algorithms | Scattering | Eigenvalues | Segments | Acceleration | Preconditioning | Regularization

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 operators H(K...

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

Czechoslovak Mathematical Journal, ISSN 0011-4642, 6/2011, Volume 61, Issue 2, pp. 371 - 381

Let E be a complex Banach space, with the unit ball B E . We study the spectrum of a bounded weighted composition operator u C φ on H ∞(B E...

32A37 | essential norm | spectra | weighted composition operators | 47B33 | Mathematics | 46E15 | 47B38 | Ordinary Differential Equations | Convex and Discrete Geometry | Analysis | Mathematics, general | Mathematical Modeling and Industrial Mathematics | bounded analytic function spaces | ESSENTIAL NORMS | MATHEMATICS | Yuan (China)

32A37 | essential norm | spectra | weighted composition operators | 47B33 | Mathematics | 46E15 | 47B38 | Ordinary Differential Equations | Convex and Discrete Geometry | Analysis | Mathematics, general | Mathematical Modeling and Industrial Mathematics | bounded analytic function spaces | ESSENTIAL NORMS | MATHEMATICS | Yuan (China)

Journal Article

Siberian Electronic Mathematical Reports, 2014, Volume 11, pp. 334 - 344

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 02/2016, Volume 289, Issue 2-3, pp. 343 - 359

.... Several sufficient conditions for a real point to be in the essential spectrum are obtained in terms of the number of linearly independent square...

essential spectrum | Primary: 34B20 | defect index | 34L05; Secondary: 47E05 | Singular discrete linear Hamiltonian system | Essential spectrum | Defect index | 2ND-ORDER DIFFERENCE-EQUATIONS | CONSTANT-COEFFICIENTS | SYMPLECTIC SYSTEMS | WEYL-TITCHMARSH THEORY | SELF-ADJOINT EXTENSIONS | JACOBI | MATHEMATICS | DEFICIENCY-INDEXES | SUBSPACES | OPERATORS | SQUARE-INTEGRABLE SOLUTIONS

essential spectrum | Primary: 34B20 | defect index | 34L05; Secondary: 47E05 | Singular discrete linear Hamiltonian system | Essential spectrum | Defect index | 2ND-ORDER DIFFERENCE-EQUATIONS | CONSTANT-COEFFICIENTS | SYMPLECTIC SYSTEMS | WEYL-TITCHMARSH THEORY | SELF-ADJOINT EXTENSIONS | JACOBI | MATHEMATICS | DEFICIENCY-INDEXES | SUBSPACES | OPERATORS | SQUARE-INTEGRABLE SOLUTIONS

Journal Article

St. Petersburg Mathematical Journal, ISSN 1061-0022, 12/2012, Volume 23, Issue 6, pp. 1023 - 1045

...: two parallel strips-uprights of thickness h>0 small, a gap is always opened between the second and third segments of the essential spectrum of the problem operator...

Periodic junction of thin domains | Dirichlet problem | Discrete spectrum | Gaps | Essential spectrum | MATHEMATICS | essential spectrum | STATES | discrete spectrum | BOUNDARY-VALUE-PROBLEMS | gaps | QUANTUM WAVE-GUIDES

Periodic junction of thin domains | Dirichlet problem | Discrete spectrum | Gaps | Essential spectrum | MATHEMATICS | essential spectrum | STATES | discrete spectrum | BOUNDARY-VALUE-PROBLEMS | gaps | QUANTUM WAVE-GUIDES

Journal Article

Siberian Electronic Mathematical Reports, 2015, Volume 12, pp. 168 - 184

Journal Article

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