Journal of Functional Analysis, ISSN 0022-1236, 02/2015, Volume 268, Issue 3, pp. 634 - 670

We construct in this article a class of closed semi-bounded quadratic forms on the space of square integrable functions over a smooth Riemannian manifold with...

Boundary conditions | Laplace–Beltrami operator | Quadratic forms | Self-adjoint extensions | Laplace-Beltrami operator | SPECTRAL GAPS | MATHEMATICS | DIFFERENTIAL-OPERATORS

Boundary conditions | Laplace–Beltrami operator | Quadratic forms | Self-adjoint extensions | Laplace-Beltrami operator | SPECTRAL GAPS | MATHEMATICS | DIFFERENTIAL-OPERATORS

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 7/2019, Volume 13, Issue 5, pp. 2259 - 2267

In this report we study a fractional analogue of Sturm–Liouville equation. A class of self-adjoint fractional Sturm–Liouville operators is described. We give a...

Riemann–Liouville derivative | The extension theory | Self-adjoint problem | Mathematics | Operator Theory | Conservation law | 47G20 | 34K08 | Analysis | Caputo derivative | Mathematics, general | Fractional kinetic equation | 45J05 | Green’s formula | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Liouville derivative | Green's formula | Environmental law

Riemann–Liouville derivative | The extension theory | Self-adjoint problem | Mathematics | Operator Theory | Conservation law | 47G20 | 34K08 | Analysis | Caputo derivative | Mathematics, general | Fractional kinetic equation | 45J05 | Green’s formula | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Liouville derivative | Green's formula | Environmental law

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 10/2018, Volume 275, Issue 7, pp. 1808 - 1888

The spectral properties of non-self-adjoint extensions of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary...

Weyl function | Differential operator | Spectral enclosure | Non-self-adjoint extension | STRONG DELTA-INTERACTION | CLOSED EXTENSIONS | GENERALIZED RESOLVENTS | SECTORIAL EXTENSIONS | BOUNDARY-VALUE-PROBLEMS | MATHEMATICS | TO-NEUMANN OPERATOR | DIFFERENTIAL-OPERATORS | EIGENVALUE BOUNDS | SCHRODINGER-OPERATORS | QUANTUM GRAPHS | Nuclear physics | Mathematics - Spectral Theory | Naturvetenskap | Mathematics | Natural Sciences | Matematik

Weyl function | Differential operator | Spectral enclosure | Non-self-adjoint extension | STRONG DELTA-INTERACTION | CLOSED EXTENSIONS | GENERALIZED RESOLVENTS | SECTORIAL EXTENSIONS | BOUNDARY-VALUE-PROBLEMS | MATHEMATICS | TO-NEUMANN OPERATOR | DIFFERENTIAL-OPERATORS | EIGENVALUE BOUNDS | SCHRODINGER-OPERATORS | QUANTUM GRAPHS | Nuclear physics | Mathematics - Spectral Theory | Naturvetenskap | Mathematics | Natural Sciences | Matematik

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2016, Volume 440, Issue 1, pp. 323 - 350

All self-adjoint extensions of minimal linear relation associated with the discrete symplectic system are characterized. Especially, for the scalar case on a...

Limit point criterion | Self-adjoint extension | Linear relation | Discrete symplectic system | Krein–von Neumann extension | Uniqueness | Krein-von Neumann extension | MATHEMATICS, APPLIED | KREIN | EQUATIONS | ORDINARY DIFFERENTIAL-OPERATORS | MATHEMATICS | SYMMETRIC SUBSPACES | HAMILTONIAN-SYSTEMS | COEFFICIENTS | FRIEDRICHS EXTENSION | Mathematics - Spectral Theory

Limit point criterion | Self-adjoint extension | Linear relation | Discrete symplectic system | Krein–von Neumann extension | Uniqueness | Krein-von Neumann extension | MATHEMATICS, APPLIED | KREIN | EQUATIONS | ORDINARY DIFFERENTIAL-OPERATORS | MATHEMATICS | SYMMETRIC SUBSPACES | HAMILTONIAN-SYSTEMS | COEFFICIENTS | FRIEDRICHS EXTENSION | Mathematics - Spectral Theory

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2017, Volume 347, pp. 235 - 260

A numerical scheme to compute the spectrum of a large class of self-adjoint extensions of the Laplace–Beltrami operator on manifolds with boundary in any...

Finite element method | Boundary conditions | Spectral problem | Self-adjoint extensions | Higher dimension | Laplace | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MATHEMATICAL | HYBRID | Methods | Algorithms

Finite element method | Boundary conditions | Spectral problem | Self-adjoint extensions | Higher dimension | Laplace | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MATHEMATICAL | HYBRID | Methods | Algorithms

Journal Article

SYMMETRY-BASEL, ISSN 2073-8994, 08/2019, Volume 11, Issue 8, p. 1047

An analysis of the invariance properties of self-adjoint extensions of symmetric operators under the action of a group of symmetries is presented. For a given...

groups of symmetry | quantum circuits | self-adjoint extensions | SPECTRAL PROBLEM | MULTIDISCIPLINARY SCIENCES | BELTRAMI OPERATOR

groups of symmetry | quantum circuits | self-adjoint extensions | SPECTRAL PROBLEM | MULTIDISCIPLINARY SCIENCES | BELTRAMI OPERATOR

Journal Article

Integral equations and operator theory, ISSN 0378-620X, 08/2018, Volume 90, Issue 4, p. 1

Let S be a symmetric operator with finite and equal defect numbers in the Hilbert space . We study the compressions of the self-adjoint extensions of S in some...

Compression | GENERALIZED RESOLVENTS | Symmetric and self-adjoint operators | Krein's resolvent formula | Q-function | Self-adjoint extension | Hilbert space | HILBERT-SPACE | Generalized resolvent | LINEAR RELATIONS | To be checked by Faculty | MATHEMATICS | Computer science | Analysis

Compression | GENERALIZED RESOLVENTS | Symmetric and self-adjoint operators | Krein's resolvent formula | Q-function | Self-adjoint extension | Hilbert space | HILBERT-SPACE | Generalized resolvent | LINEAR RELATIONS | To be checked by Faculty | MATHEMATICS | Computer science | Analysis

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 1/2018, Volume 108, Issue 1, pp. 195 - 212

We establish a bijection between the self-adjoint extensions of the Laplace operator on a bounded regular domain and the unitary operators on the boundary....

Geometry | Quantum boundary conditions | 47A07 | Quadratic forms | Theoretical, Mathematical and Computational Physics | Complex Systems | Self-adjoint extensions | Group Theory and Generalizations | 81Q10 | 35J25 | Physics | PHYSICS, MATHEMATICAL

Geometry | Quantum boundary conditions | 47A07 | Quadratic forms | Theoretical, Mathematical and Computational Physics | Complex Systems | Self-adjoint extensions | Group Theory and Generalizations | 81Q10 | 35J25 | Physics | PHYSICS, MATHEMATICAL

Journal Article

Thai Journal of Mathematics, ISSN 1686-0209, 04/2018, Volume 16, Issue 1, pp. 275 - 285

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 02/2008, Volume 20, Issue 1, pp. 1 - 70

We give a self-contained presentation of the theory of self-adjoint extensions using the technique of boundary triples. A description of the spectra of...

Point perturbations | Spectral measure | Self-adjoint extensions | Weyl function | Quantum graphs | Self-adjoint operators | Spectrum | point perturbations | quantum graphs | GENERALIZED RESOLVENTS | self-adjoint extensions | self-adjoint operators | VALUED HERGLOTZ FUNCTIONS | BOUNDARY-VALUE-PROBLEMS | CONTINUITY PROPERTIES | SINGULAR INTERACTIONS | PHYSICS, MATHEMATICAL | spectral measure | DIFFERENTIAL OPERATORS | SYMMETRIC-OPERATORS | spectrum | MAGNETIC-FIELD | KREINS RESOLVENT FORMULA

Point perturbations | Spectral measure | Self-adjoint extensions | Weyl function | Quantum graphs | Self-adjoint operators | Spectrum | point perturbations | quantum graphs | GENERALIZED RESOLVENTS | self-adjoint extensions | self-adjoint operators | VALUED HERGLOTZ FUNCTIONS | BOUNDARY-VALUE-PROBLEMS | CONTINUITY PROPERTIES | SINGULAR INTERACTIONS | PHYSICS, MATHEMATICAL | spectral measure | DIFFERENTIAL OPERATORS | SYMMETRIC-OPERATORS | spectrum | MAGNETIC-FIELD | KREINS RESOLVENT FORMULA

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 03/2018, Volume 41, Issue 5, pp. 1761 - 1773

In this paper, we construct a space of boundary values for minimal symmetric 1D Hamiltonian operator with defect index (1,1) (in limit‐point case at a(b) and...

functional model | maximal dissipative operator | scattering matrix | self‐adjoint dilation | 1D singular Hamiltonian system | extensions of symmetric operator | completeness of the system of root vectors | characteristic function | self-adjoint dilation | MATHEMATICS, APPLIED | FUNCTIONAL MODELS | DIRAC OPERATORS | Operators | Dissipation | Dilation | Eigenvalues | Hilbert space | Hamiltonian functions | Characteristic functions

functional model | maximal dissipative operator | scattering matrix | self‐adjoint dilation | 1D singular Hamiltonian system | extensions of symmetric operator | completeness of the system of root vectors | characteristic function | self-adjoint dilation | MATHEMATICS, APPLIED | FUNCTIONAL MODELS | DIRAC OPERATORS | Operators | Dissipation | Dilation | Eigenvalues | Hilbert space | Hamiltonian functions | Characteristic functions

Journal Article

ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 03/2018, Volume 52, Issue 2, pp. 481 - 508

In this work we deal with a scalar spectral mixed boundary value problem in a spacial junction of thin rods and a plate. Constructing asymptotics of the...

Dimension reduction | Scalar spectral problem | Asymptotics | Function space with detached asymptotics | Junction of thin rods and plate | Self-adjoint extensions of differential operators | MATHEMATICS, APPLIED | self-adjoint extensions of differential operators | asymptotics | BOUNDARY-VALUE-PROBLEMS | function space with detached asymptotics | dimension reduction | scalar spectral problem | Mathematics - Analysis of PDEs

Dimension reduction | Scalar spectral problem | Asymptotics | Function space with detached asymptotics | Junction of thin rods and plate | Self-adjoint extensions of differential operators | MATHEMATICS, APPLIED | self-adjoint extensions of differential operators | asymptotics | BOUNDARY-VALUE-PROBLEMS | function space with detached asymptotics | dimension reduction | scalar spectral problem | Mathematics - Analysis of PDEs

Journal Article

13.
Full Text
From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code

Annals of Physics, ISSN 0003-4916, 10/2015, Volume 361, pp. 303 - 329

We regularize compact and non-compact Abelian Chern–Simons–Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled...

Self-adjoint extension | Quantum information | Berry gauge field | Toric code | Chern–Simons theory | Lattice gauge theory | Chern-Simons theory | FRACTIONAL STATISTICS | SPIN | PHYSICS, MULTIDISCIPLINARY | TRAPPED IONS | QUANTUM-FIELD THEORY | CONSTANT MAGNETIC-FIELD | DIMENSIONS | MODELS | ANYONS | COMPUTATION | QUANTIZATION | Contact lenses | Lattice theory

Self-adjoint extension | Quantum information | Berry gauge field | Toric code | Chern–Simons theory | Lattice gauge theory | Chern-Simons theory | FRACTIONAL STATISTICS | SPIN | PHYSICS, MULTIDISCIPLINARY | TRAPPED IONS | QUANTUM-FIELD THEORY | CONSTANT MAGNETIC-FIELD | DIMENSIONS | MODELS | ANYONS | COMPUTATION | QUANTIZATION | Contact lenses | Lattice theory

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 06/2012, Volume 53, Issue 6, p. 63505

A model of the point-like interaction between the classical electromagnetic field and the quantum electron is suggested. It is based on the theory of...

POINT INTERACTIONS | PHYSICS, MATHEMATICAL | SCATTERING | SELF-ADJOINT EXTENSIONS

POINT INTERACTIONS | PHYSICS, MATHEMATICAL | SCATTERING | SELF-ADJOINT EXTENSIONS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 08/2014, Volume 454, pp. 1 - 48

This paper is concerned with self-adjoint extensions for a class of discrete linear Hamiltonian systems. By applying the generalized von Neumann theory and the...

Self-adjoint extension | Limit circle case | Defect index | Discrete linear Hamiltonian system | Limit point case | MATHEMATICS, APPLIED | SUBSPACES | POINT | M(LAMBDA) THEORY

Self-adjoint extension | Limit circle case | Defect index | Discrete linear Hamiltonian system | Limit point case | MATHEMATICS, APPLIED | SUBSPACES | POINT | M(LAMBDA) THEORY

Journal Article

OPERATORS AND MATRICES, ISSN 1846-3886, 2008, Volume 2, Issue 4, pp. 483 - 506

We provide a simple recipe for obtaining all self-adjoint extensions, together with their resolvent, of the symmetric operator S obtained by restricting the...

elliptic boundary value problems | MATHEMATICS | SINGULAR PERTURBATIONS | RESOLVENTS | BOUNDARY-CONDITIONS | Self-adjoint extensions | Krein's resolvent formula | FORMULA | OPERATORS

elliptic boundary value problems | MATHEMATICS | SINGULAR PERTURBATIONS | RESOLVENTS | BOUNDARY-CONDITIONS | Self-adjoint extensions | Krein's resolvent formula | FORMULA | OPERATORS

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 9/2015, Volume 15, Issue 3, pp. 727 - 751

Given a linear semi-bounded symmetric operator $${S\ge -\omega}$$ S ≥ - ω , we explicitly define, and provide their nonlinear resolvents, nonlinear maximal...

35J65 | 35J87 | Nonlinear extensions | Nonlinear boundary conditions | Analysis | Mathematics | Nonlinear singular perturbations | 47H05 | Nonlinear resolvent formulae | SINGULAR PERTURBATIONS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | SELF-ADJOINT EXTENSIONS | MATHEMATICS | SEMIGROUPS | DIFFERENTIAL-OPERATORS | DOMAINS

35J65 | 35J87 | Nonlinear extensions | Nonlinear boundary conditions | Analysis | Mathematics | Nonlinear singular perturbations | 47H05 | Nonlinear resolvent formulae | SINGULAR PERTURBATIONS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | SELF-ADJOINT EXTENSIONS | MATHEMATICS | SEMIGROUPS | DIFFERENTIAL-OPERATORS | DOMAINS

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2018, Volume 108, Issue 12, pp. 2635 - 2667

We describe the self-adjoint realizations of the operator $$H:=-i\alpha \cdot \nabla + m\beta + \mathbb {V}(x)$$ H:=-iα·∇+mβ+V(x) , for $$m\in \mathbb {R}$$...

Coulomb potential | Theoretical, Mathematical and Computational Physics | Complex Systems | Hardy inequality | Physics | Geometry | 47N50 | Self-adjoint operator | Primary 81Q10 | 47B25 | Group Theory and Generalizations | Dirac operator | Secondary 47N20 | ESSENTIAL SELFADJOINTNESS | ESSENTIAL SPECTRUM | PHYSICS, MATHEMATICAL | Mathematics - Analysis of PDEs

Coulomb potential | Theoretical, Mathematical and Computational Physics | Complex Systems | Hardy inequality | Physics | Geometry | 47N50 | Self-adjoint operator | Primary 81Q10 | 47B25 | Group Theory and Generalizations | Dirac operator | Secondary 47N20 | ESSENTIAL SELFADJOINTNESS | ESSENTIAL SPECTRUM | PHYSICS, MATHEMATICAL | Mathematics - Analysis of PDEs

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2011, Volume 434, Issue 4, pp. 903 - 930

In this paper, self-adjoint extensions for second-order symmetric linear difference equations with real coefficients are studied. By applying the...

Self-adjoint operator extension | Symmetric linear difference equation | Glazman–Krein–Naimark theory | Self-adjoint subspace extension | Glazman-Krein-Naimark theory | CRITERIA | EIGENVALUES | MATHEMATICS, APPLIED | BOUNDARY-CONDITIONS | HAMILTONIAN-SYSTEMS | MATRICES | DIMENSIONAL SCHRODINGER-OPERATORS | ABSOLUTELY CONTINUOUS-SPECTRUM

Self-adjoint operator extension | Symmetric linear difference equation | Glazman–Krein–Naimark theory | Self-adjoint subspace extension | Glazman-Krein-Naimark theory | CRITERIA | EIGENVALUES | MATHEMATICS, APPLIED | BOUNDARY-CONDITIONS | HAMILTONIAN-SYSTEMS | MATRICES | DIMENSIONAL SCHRODINGER-OPERATORS | ABSOLUTELY CONTINUOUS-SPECTRUM

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 12/2014, Volume 462, pp. 204 - 232

This paper is concerned with -self-adjoint extensions for a class of Hamiltonian differential systems. The domains of the corresponding minimal and maximal...

[formula omitted]-self-adjoint extension | Hamiltonian system | [formula omitted]-defect index | [formula omitted]-symmetric | J-self-adjoint extension | J-symmetric | J-defect index | MATHEMATICS, APPLIED | EQUATIONS | SPECTRAL EXACTNESS | DIRAC-TYPE OPERATORS | M(LAMBDA) THEORY | MATHEMATICS | ORDER | J-SELFADJOINT EXTENSIONS | COMPLEX COEFFICIENTS | INCLUSION | SQUARE-INTEGRABLE SOLUTIONS | J-SYMMETRIC OPERATORS

[formula omitted]-self-adjoint extension | Hamiltonian system | [formula omitted]-defect index | [formula omitted]-symmetric | J-self-adjoint extension | J-symmetric | J-defect index | MATHEMATICS, APPLIED | EQUATIONS | SPECTRAL EXACTNESS | DIRAC-TYPE OPERATORS | M(LAMBDA) THEORY | MATHEMATICS | ORDER | J-SELFADJOINT EXTENSIONS | COMPLEX COEFFICIENTS | INCLUSION | SQUARE-INTEGRABLE SOLUTIONS | J-SYMMETRIC OPERATORS

Journal Article