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Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems

Journal of functional analysis, ISSN 0022-1236, 2014, Volume 266, Issue 7, pp. 4037 - 4100

The theory of selfadjoint extensions of symmetric operators, and more generally the theory of extensions of dual pairs, was implemented some years ago for boundary value problems for elliptic...

Nonsmooth coefficients | Elliptic boundary value problems | Extension theory | Symbol smoothing | M-functions | Krein resolvent formula | Pseudodifferential boundary operators | Nonsmooth domains | EQUATIONS | PSEUDODIFFERENTIAL-OPERATORS | MATHEMATICS | SOBOLEV SPACES | BESOV | COEFFICIENTS | DOMAINS

Nonsmooth coefficients | Elliptic boundary value problems | Extension theory | Symbol smoothing | M-functions | Krein resolvent formula | Pseudodifferential boundary operators | Nonsmooth domains | EQUATIONS | PSEUDODIFFERENTIAL-OPERATORS | MATHEMATICS | SOBOLEV SPACES | BESOV | COEFFICIENTS | DOMAINS

Journal Article

Journal of Mathematical Sciences (United States), ISSN 1072-3374, 06/2017, Volume 224, Issue 4, pp. 1 - 16

A generalization of the well-known results of M.G. Krein on the description of the self-adjoint contractive extension of a Hermitian contraction is obtained...

Kreĭn and Pontryagin spaces | Completion | extension of operators | Extension of operators

Kreĭn and Pontryagin spaces | Completion | extension of operators | Extension of operators

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 9/2018, Volume 18, Issue 3, pp. 1341 - 1379

...: a Courant–Hilbert nodal line theorem for harmonic extensions of the eigenfunctions of non-local...

Non-local operator | 60J75 | Extension technique | Secondary 60J60 | Primary 35J25 | 47G20 | Analysis | Complete Bernstein function | 35J70 | Mathematics | Fractional Laplacian | Krein’s string | MATHEMATICS, APPLIED | DIFFUSIONS | EIGENFUNCTIONS | NONLOCAL SCHRODINGER-OPERATORS | MATHEMATICS | SEMIGROUPS | Krein's string | TRACES | CAUCHY PROCESS | CONFORMAL GEOMETRY | SYMMETRIC STABLE PROCESSES

Non-local operator | 60J75 | Extension technique | Secondary 60J60 | Primary 35J25 | 47G20 | Analysis | Complete Bernstein function | 35J70 | Mathematics | Fractional Laplacian | Krein’s string | MATHEMATICS, APPLIED | DIFFUSIONS | EIGENFUNCTIONS | NONLOCAL SCHRODINGER-OPERATORS | MATHEMATICS | SEMIGROUPS | Krein's string | TRACES | CAUCHY PROCESS | CONFORMAL GEOMETRY | SYMMETRIC STABLE PROCESSES

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...

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

Annals of physics, ISSN 0003-4916, 2012, Volume 327, Issue 10, pp. 2411 - 2431

In some recent articles, we developed a new systematic approach to generate solvable rational extensions of primary translationally shape invariant potentials...

Exceptional orthogonal polynomial | Disconjugacy | Krein–Adler theorem | Supersymmetric quantum mechanics | Shape invariance | Darboux transformation | Krein-Adler theorem | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | SCHRODINGER-EQUATION | LAGUERRE | EXACTLY SOLVABLE POTENTIALS | ANHARMONIC-OSCILLATORS | SHAPE-INVARIANT POTENTIALS | ORTHOGONAL POLYNOMIALS | QUANTUM-MECHANICS | SPECTRA | DARBOUX TRANSFORMATIONS | Rational expectations | Polynomials | Phase transitions | Physics | Variances | Eigen values | EXCITED STATES | LAGUERRE POLYNOMIALS | SCHROEDINGER EQUATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | OSCILLATORS | EIGENSTATES | HAMILTONIANS | POTENTIALS | QUANTUM MECHANICS | TRANSFORMATIONS

Exceptional orthogonal polynomial | Disconjugacy | Krein–Adler theorem | Supersymmetric quantum mechanics | Shape invariance | Darboux transformation | Krein-Adler theorem | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | SCHRODINGER-EQUATION | LAGUERRE | EXACTLY SOLVABLE POTENTIALS | ANHARMONIC-OSCILLATORS | SHAPE-INVARIANT POTENTIALS | ORTHOGONAL POLYNOMIALS | QUANTUM-MECHANICS | SPECTRA | DARBOUX TRANSFORMATIONS | Rational expectations | Polynomials | Phase transitions | Physics | Variances | Eigen values | EXCITED STATES | LAGUERRE POLYNOMIALS | SCHROEDINGER EQUATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | OSCILLATORS | EIGENSTATES | HAMILTONIANS | POTENTIALS | QUANTUM MECHANICS | TRANSFORMATIONS

Journal Article

Acta mathematica Hungarica, ISSN 1588-2632, 2011, Volume 135, Issue 1-2, pp. 116 - 129

...: T ∗ T always admits a positive selfadjoint extension. The Friedrichs extension also will be obtained whenever...

47B25 | operator extension | Mathematics, general | Mathematics | Friedrichs extension | 47A20 | positive operator | Krein–von Neumann extension | selfadjoint operator | closable operator | MATHEMATICS | Krein-von Neumann extension | OPERATORS

47B25 | operator extension | Mathematics, general | Mathematics | Friedrichs extension | 47A20 | positive operator | Krein–von Neumann extension | selfadjoint operator | closable operator | MATHEMATICS | Krein-von Neumann extension | OPERATORS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2017, Volume 304, pp. 1108 - 1155

...), associated with the differential expressionτ2m(a,b,q):=(∑j,k=1n(−i∂j−bj)aj,k(−i∂k−bk)+q)m,m∈N, and its Krein–von Neumann extension AK...

Buckling problem | Bounds on eigenvalue counting functions | Krein and Friedrichs extensions of powers of second-order uniformly elliptic partial differential operators | Spectral analysis | MAGNETIC POTENTIALS | STRICHARTZ | EIGENFUNCTION-EXPANSIONS | SCATTERING-THEORY | RIESZ MEANS | LAPLACIAN | MATHEMATICS | RESOLVENT | Bounds on eigenvalue counting functions Spectral analysis | FORMULAS | EQUATION | SCHRODINGER-OPERATORS

Buckling problem | Bounds on eigenvalue counting functions | Krein and Friedrichs extensions of powers of second-order uniformly elliptic partial differential operators | Spectral analysis | MAGNETIC POTENTIALS | STRICHARTZ | EIGENFUNCTION-EXPANSIONS | SCATTERING-THEORY | RIESZ MEANS | LAPLACIAN | MATHEMATICS | RESOLVENT | Bounds on eigenvalue counting functions Spectral analysis | FORMULAS | EQUATION | SCHRODINGER-OPERATORS

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 04/2012, Volume 135, Issue 1-2, pp. 116 - 129

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...

Point perturbations | Spectral measure | Self-adjoint extensions | Weyl function | Quantum graphs | Self-adjoint operators | Spectrum | point perturbations | SYSTEM | quantum graphs | GENERALIZED RESOLVENTS | PERTURBATIONS | self-adjoint extensions | self-adjoint operators | BOUNDARY-VALUE-PROBLEMS | CONTINUITY PROPERTIES | PHYSICS, MATHEMATICAL | spectral measure | DIFFERENTIAL OPERATORS | SYMMETRIC-OPERATORS | spectrum | KREINS RESOLVENT FORMULA | SCATTERING

Point perturbations | Spectral measure | Self-adjoint extensions | Weyl function | Quantum graphs | Self-adjoint operators | Spectrum | point perturbations | SYSTEM | quantum graphs | GENERALIZED RESOLVENTS | PERTURBATIONS | self-adjoint extensions | self-adjoint operators | BOUNDARY-VALUE-PROBLEMS | CONTINUITY PROPERTIES | PHYSICS, MATHEMATICAL | spectral measure | DIFFERENTIAL OPERATORS | SYMMETRIC-OPERATORS | spectrum | KREINS RESOLVENT FORMULA | SCATTERING

Journal Article

Banach journal of mathematical analysis, ISSN 1735-8787, 2019, Volume 13, Issue 3, pp. 538 - 564

In this paper we consider sectorial operators, or more generally, sectorial relations and their maximal-sectorial extensions in a Hilbert space H...

Krein extension | sectorial relation | Friedrichs extension | form sum | OPERATORS | To be checked by Faculty | extremal extension | MATHEMATICS | MATHEMATICS, APPLIED

Krein extension | sectorial relation | Friedrichs extension | form sum | OPERATORS | To be checked by Faculty | extremal extension | MATHEMATICS | MATHEMATICS, APPLIED

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...

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

Journal of Mathematical Physics, Analysis, Geometry, ISSN 1812-9471, 2017, Volume 13, Issue 3, pp. 205 - 241

We study maximal sectorial extensions of an arbitrary closed densely de fined sectorial operator...

Boundary pair | Kreĭn-von Neumann extension | Friedrichs extension | Accretive operator | Boundary triplet | Sectorial operator | accretive operator | Krein-von Neumann extension | HERMITIAN OPERATORS | boundary pair | boundary triplet | sectorial operator | PHYSICS, MATHEMATICAL

Boundary pair | Kreĭn-von Neumann extension | Friedrichs extension | Accretive operator | Boundary triplet | Sectorial operator | accretive operator | Krein-von Neumann extension | HERMITIAN OPERATORS | boundary pair | boundary triplet | sectorial operator | PHYSICS, MATHEMATICAL

Journal Article

Acta mathematica Hungarica, ISSN 1588-2632, 2011, Volume 135, Issue 4, pp. 325 - 341

...–von Neumann extension, the smallest among all positive selfadjoint extensions, has closed range...

closed range | Moore–Penrose inverse | operator extension | 47B65 | Mathematics, general | Mathematics | Friedrichs extension | 47A20 | positive operator | Krein–von Neumann extension | Krein-von Neumann extension | Moore-Penrose inverse | MATHEMATICS | PSEUDO-INVERSE

closed range | Moore–Penrose inverse | operator extension | 47B65 | Mathematics, general | Mathematics | Friedrichs extension | 47A20 | positive operator | Krein–von Neumann extension | Krein-von Neumann extension | Moore-Penrose inverse | MATHEMATICS | PSEUDO-INVERSE

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 02/2010, Volume 283, Issue 2, pp. 165 - 179

We prove the unitary equivalence of the inverse of the Krein–von Neumann extension...

Krein−von Neumann extension | buckling problem | Buckling problem | Krein-von Neumann extension | NONNEGATIVE OPERATORS | MATHEMATICS | DIFFERENTIAL-OPERATORS

Krein−von Neumann extension | buckling problem | Buckling problem | Krein-von Neumann extension | NONNEGATIVE OPERATORS | MATHEMATICS | DIFFERENTIAL-OPERATORS

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 06/2014, Volume 287, Issue 8-9, pp. 869 - 884

...‐adjoint extensions, i.e., the so‐called Friedrichs and Kreĭn extensions. We show that for the interval of parameters under consideration, the Friedrichs extension...

self‐adjoint | Kreĭn extension | 47B39 | q‐difference operator | 47B25 | 39A13 | 47B37 | 39A12 | 34N05 | scale‐invariant | Friedrichs extension | Kreǐn extension | Self-adjoint | q-difference operator | Scale-invariant | MATHEMATICS | self-adjoint | Krein extension | EQUATIONS | scale-invariant

self‐adjoint | Kreĭn extension | 47B39 | q‐difference operator | 47B25 | 39A13 | 47B37 | 39A12 | 34N05 | scale‐invariant | Friedrichs extension | Kreǐn extension | Self-adjoint | q-difference operator | Scale-invariant | MATHEMATICS | self-adjoint | Krein extension | EQUATIONS | scale-invariant

Journal Article

1990, Operator theory, advances and applications, ISBN 0817625305, Volume 47., vii, 305 p. :$bill. ;$c24 cm.

Book

Complex analysis and operator theory, ISSN 1661-8262, 2012, Volume 8, Issue 3, pp. 591 - 663

We study restriction and extension theory for semibounded Hermitian operators in the Hardy space $$\fancyscript{H}_{2...

Shannon kernel | Analytic functions | Hurwitz zeta-function | Unitary one-parameter group | Boundary values | Spectral transforms | Scattering operator | Mathematics | Szegö kernel | Unbounded operators | 35Q40 | 42C10 | Hilbert transform | Operator Theory | 46F12 | 47B25 | Lax-Phillips | 47L60 | Poisson-kernel | 47A25 | Mathematics, general | Hilbert space | Exponential polynomials | Quadratic form | Friedrichs | Quantum states | Fourier analysis | 34L25 | Deficiency-indices | Quantum-tunneling | Spectral representation | Scattering theory | 35F15 | Semibounded operator | Extension | 81U35 | Krein | Analysis | Scattering poles | 81Q35 | Reproducing kernels | Discrete spectrum | 46L45 | Hardy space | MATHEMATICS, APPLIED | KERNEL HILBERT-SPACES | MATHEMATICS | ADJOINT | Szego kernel | DEFICIENCY-INDEXES | Atmospheric physics

Shannon kernel | Analytic functions | Hurwitz zeta-function | Unitary one-parameter group | Boundary values | Spectral transforms | Scattering operator | Mathematics | Szegö kernel | Unbounded operators | 35Q40 | 42C10 | Hilbert transform | Operator Theory | 46F12 | 47B25 | Lax-Phillips | 47L60 | Poisson-kernel | 47A25 | Mathematics, general | Hilbert space | Exponential polynomials | Quadratic form | Friedrichs | Quantum states | Fourier analysis | 34L25 | Deficiency-indices | Quantum-tunneling | Spectral representation | Scattering theory | 35F15 | Semibounded operator | Extension | 81U35 | Krein | Analysis | Scattering poles | 81Q35 | Reproducing kernels | Discrete spectrum | 46L45 | Hardy space | MATHEMATICS, APPLIED | KERNEL HILBERT-SPACES | MATHEMATICS | ADJOINT | Szego kernel | DEFICIENCY-INDEXES | Atmospheric physics

Journal Article

Revista Matemática Iberoamericana, ISSN 0213-2230, 2006, Volume 22, Issue 1, pp. 93 - 110

Let $X$ be a Banach space, $u\in X^{**}$ and $K, Z$ two subsets of $X^{**}$. Denote by $d(u,Z)$ and $d(K,Z)$ the distances to $Z$ from the point $u$ and from...

General | Functional analysis | Compact sets | Banach spaces | Krein-Smulian Theorem | MATHEMATICS | COMPACT SPACES | compact sets | BANACH-SPACES | 46B20 | 46B26 | Krein-Šmulian Theorem

General | Functional analysis | Compact sets | Banach spaces | Krein-Smulian Theorem | MATHEMATICS | COMPACT SPACES | compact sets | BANACH-SPACES | 46B20 | 46B26 | Krein-Šmulian Theorem

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 10/2016, Volume 10, Issue 7, pp. 1535 - 1550

We provide a streamlined construction of the Friedrichs extension of a densely-defined self-adjoint and semibounded operator A on a Hilbert space $$\mathcal {H...

Graph energy | 05C50 | Krein extension | 47B32 | Mathematics | Graph Laplacian | Operator Theory | 47B25 | Mathematics, general | Defect indices | Hilbert space | 60J10 | Resistance network | 05C63 | Effective resistance | Essentially self-adjoint | Spectral graph theory | Reproducing kernel | Unbounded linear operator | Symmetric pair | 47B39 | Spectral resolution | 46E22 | 47B15 | Analysis | 46B22 | Self-adjoint extension | Friedrichs extension | MATHEMATICS, APPLIED | MATHEMATICS

Graph energy | 05C50 | Krein extension | 47B32 | Mathematics | Graph Laplacian | Operator Theory | 47B25 | Mathematics, general | Defect indices | Hilbert space | 60J10 | Resistance network | 05C63 | Effective resistance | Essentially self-adjoint | Spectral graph theory | Reproducing kernel | Unbounded linear operator | Symmetric pair | 47B39 | Spectral resolution | 46E22 | 47B15 | Analysis | 46B22 | Self-adjoint extension | Friedrichs extension | MATHEMATICS, APPLIED | MATHEMATICS

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 02/2013, Volume 286, Issue 2‐3, pp. 118 - 148

A description of all exit space extensions with finitely many negative squares of a symmetric operator of defect one is given via Krein's formula...

30E20 | Generalized Nevanlinna function | Krein's formula | 30D50 | definitizable function | Krein space | 47B50 | 34B07 | matrix valued function | Weyl function | boundary triplet | MSC | operator with finitely many negative squares | symmetric and self‐adjoint operator | Definitizable function | Matrix valued function | Operator with finitely many negative squares | Symmetric and self-adjoint operator | Boundary triplet | symmetric and self-adjoint operator | MATRIX FUNCTIONS | FACTORIZATION | REPRESENTATIONS | GENERALIZED NEVANLINNA FUNCTIONS | MATHEMATICS | EIGENVALUES | DEPENDING BOUNDARY-CONDITIONS | STURM-LIOUVILLE OPERATORS | RESOLVENTS | SYMMETRIC-OPERATORS

30E20 | Generalized Nevanlinna function | Krein's formula | 30D50 | definitizable function | Krein space | 47B50 | 34B07 | matrix valued function | Weyl function | boundary triplet | MSC | operator with finitely many negative squares | symmetric and self‐adjoint operator | Definitizable function | Matrix valued function | Operator with finitely many negative squares | Symmetric and self-adjoint operator | Boundary triplet | symmetric and self-adjoint operator | MATRIX FUNCTIONS | FACTORIZATION | REPRESENTATIONS | GENERALIZED NEVANLINNA FUNCTIONS | MATHEMATICS | EIGENVALUES | DEPENDING BOUNDARY-CONDITIONS | STURM-LIOUVILLE OPERATORS | RESOLVENTS | SYMMETRIC-OPERATORS

Journal Article

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