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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN 0022-247X, 02/2015, Volume 422, Issue 1, pp. 212 - 239
The exceptional X-1-Jacobi differential expression is a second-order ordinary differential expression with rational coefficients; it was discovered by... 
Glazman-Krein-Naimark theory | MATHEMATICS | MATHEMATICS, APPLIED | Spectral theory | Orthogonal polynomials | Left-definite theory | X-1-Jacobi polynomials | EQUATIONS | STIRLING NUMBERS | LAGUERRE-POLYNOMIALS | OPERATORS
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 04/2019, Volume 60, Issue 4, p. 41502
We determine explicitly a boundary triple for the Dirac operator H≔−iα⋅∇+mβ+V(x) in R3, for m∈R and V(x)=|x|−1(νI4+μβ−iλα⋅x/|x| β), with ν,μ,λ∈R. Consequently,... 
PHYSICS, MATHEMATICAL | SELF-ADJOINT EXTENSIONS | Quadratic forms
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 02/2017, Volume 49, Issue 1, pp. 148 - 164
We characterize diagonals of unbounded self‐adjoint operators on a Hilbert space H that have only discrete spectrum, that is, with empty essential spectrum.... 
46C05 | 15A42 (secondary) | 47B15 | 47B25 (primary) | DIAGONALS | MATHEMATICS | PYTHAGOREAN THEOREM | MAJORIZATION | FINITE SPECTRUM | Mathematics - Functional Analysis
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 02/2020, pp. 1 - 18
Journal Article
Mathematische Annalen, ISSN 0025-5831, 6/2012, Volume 353, Issue 2, pp. 519 - 522
If $${u \mapsto A(u)}$$ is a C 0,α -mapping, for 0 < α ≤ 1, having as values unbounded self-adjoint operators with compact resolvents and common domain of... 
Primary 47A55 | Mathematics, general | 47A56 | Mathematics | 47B25 | MATHEMATICS
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 11/2018, Volume 291, Issue 16, pp. 2489 - 2497
In this note we show that if a boundary system in the sense of (Schubert et al. 2015) gives rise to any skew‐self‐adjoint extension, then it induces a boundary... 
boundary system | Primary: 47B25 | extension problem | boundary triple | boundary triplet | Secondary: 35G15 | deficiency index | MATHEMATICS | OPERATORS
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 12/2016, Volume 289, Issue 17-18, pp. 2133 - 2146
We study the eigenvalue problem for the Neumann–Laplace operator in conformal regular planar domains Ω⊂C. Conformal regular domains support the... 
elliptic equations | 35J40 | quasidiscs | 47B25 | 35P15 | 47A75 | conformal mappings | eigenvalue problem | MATHEMATICS | EIGENVALUES | DIMENSION | OPERATORS
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 08/2017, Volume 49, Issue 4, pp. 742 - 744
A famous theorem due to Weyl and von Neumann asserts that two bounded self‐adjoint operators are unitarily equivalent modulo the compacts, if and only if their... 
47B25 (primary) | MATHEMATICS
Journal Article
Results in Mathematics, ISSN 1422-6383, 6/2019, Volume 74, Issue 2, pp. 1 - 6
A criteria due to Toivo Nieminen concerning selfadjoint linear operators in complex Hilbert spaces is extended to the case of linear relations. 
selfadjoint linear relation | 47A06 | 47B25 | Cayley transform | 47B65 | Mathematics, general | Mathematics | Hilbert space | unitary operator | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 9/2018, Volume 34, Issue 9, pp. 1473 - 1484
Symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied, the necessary and sufficient conditions are given. Using the relatively... 
relative bound | 47E05 | 47B25 | 47A05 | symplectic self-adjointness | quadratic complement | Mathematics, general | Mathematics | Hamiltonian operator | MATHEMATICS | MATHEMATICS, APPLIED | Mathematical analysis | Operators
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 11/2015, Volume 288, Issue 16, pp. 1822 - 1833
We study the eigenvalue problem for the Dirichlet Laplacian in bounded simply connected plane domains Ω⊂C by reducing it, using conformal transformations, to... 
elliptic equations | 35J40 | quasidiscs | 47B25 | 35P15 | Eigenvalue problem | 47A75 | conformal mappings | Elliptic equations | Conformal mappings | Quasidiscs | MATHEMATICS | EIGENVALUES | DIMENSION | OPERATORS
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 12/2015, Volume 83, Issue 4, pp. 451 - 482
In the present note a functional calculus $${\phi \mapsto \phi(A)}$$ ϕ ↦ ϕ ( A ) for self-adjoint definitizable linear relations on Krein spaces is developed.... 
47A06 | Spectral theorem | Definitizable linear relations | 47B25 | Analysis | Krein space | Mathematics | 47B50 | 47A60 | MATHEMATICS | OPERATORS
Journal Article
Potential Analysis, ISSN 0926-2601, 8/2018, Volume 49, Issue 2, pp. 331 - 358
In this paper, we introduce the notion of oriented faces especially triangles in a connected oriented locally finite graph. This framework then permits to... 
05C12 | 05C50 | Difference operator | 05C63 | Essential self-adjointness | Probability Theory and Stochastic Processes | Mathematics | Laplacian on forms | Geometry | Potential Theory | Functional Analysis | 47B25 | 39A12 | Infinite graph | MATHEMATICS
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
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 09/2019, Volume 292, Issue 9, pp. 1911 - 1930
Let H0=−Δ+V0(x) be a Schrödinger operator on L2(Rν), ν=1,2, or 3, where V0(x) is a bounded measurable real‐valued function on Rν. Let V be an operator of... 
resolvent comparable operators | singular μ‐invariant | spectral shift function | 47A55 | Primary: 47A40 | Secondary: 47A70 | singular spectral shift function | 81U99 | 35P05 | 47B25 | 35P25 | resonance index | stationary scattering theory | Schrödinger operators | singular mu-invariant | MATHEMATICS | Schrodinger operators
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 10/2019, Volume 91, Issue 5, pp. 1 - 17
In this paper we consider extensions of positive operators. We study the connections between the von Neumann theory of extensions and characterisations of... 
Elliptic operators | 47A07 | Secondary 35J15 | 47B25 | Aharonov–Bohm operator | Analysis | Primary 47A20 | Von Neumann theory | Mathematics | Operator extensions | Sesquilinear form | 47F05 | MATHEMATICS | Aharonov-Bohm operator | FRIEDRICHS EXTENSION | Computer science
Journal Article
Complex Variables and Elliptic Equations, ISSN 1747-6933, 09/2019, Volume 64, Issue 9, pp. 1477 - 1499
We derive a description of the family of canonical selfadjoint extensions of the operator of multiplication in a de Branges space in terms of singular rank-one... 
singular rank-one perturbations | de Branges spaces | scale of Hilbert spaces | V. Bolotnikov | 47A70 | 47B25 | 46E22 | EXISTENCE | MATHEMATICS | DEFICIENCY-INDEXES | HERMITIAN OPERATORS | Bolotnikov | SCHRODINGER-OPERATORS | Multiplication | Hilbert space
Journal Article
Periodica Mathematica Hungarica, ISSN 0031-5303, 12/2017, Volume 75, Issue 2, pp. 268 - 272
We provide a short, elementary proof of the existence and uniqueness of the square root in the context of unbounded positive selfadjoint operators on real or... 
Selfadjoint operator | Square root | Unbounded operator | 47B65 | Mathematics, general | Mathematics | Primary 47B25 | Positive operator | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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