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Self-adjoint extensions for the Dirac operator with Coulomb-type spherically symmetric potentials
, 2017We describe the self-adjoint realizations of the operator $$H:=-i\alpha \cdot \nabla + m\beta + \mathbb {V}(x)$$H:=-iα·∇+mβ+V(x), for $$m\in \mathbb {R}$$m∈R, and $$\mathbb {V}(x)= {|}x{|}^{-1} ( \nu \mathbb {I}_4 +\mu \beta -i \lambda \alpha \cdot {x}/{{
B. Cassano, Fabio Pizzichillo
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Self-adjoint Boundary Conditions for the Prolate Spheroid Differential Operator
, 2016We consider the formal prolate spheroid differential operator on a finite symmetric interval and describe all its self-adjoint boundary conditions. Only one of these boundary conditions corresponds to a self-adjoint differential operator which commute ...
V. Katsnelson
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On J-Self-Adjoint Differential Operators Similar to Self-Adjoint Operators
Mathematical Notes, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1996
In this chapter, we make a preliminary study of one of the most important classes of operators on a Hilbert space, the self-adjoint operators. These operators are the infinite-dimensional analogues of symmetric matrices. They play an essential role in quantum mechanics as they determine the time evolution of quantum states.
P. D. Hislop, I. M. Sigal
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In this chapter, we make a preliminary study of one of the most important classes of operators on a Hilbert space, the self-adjoint operators. These operators are the infinite-dimensional analogues of symmetric matrices. They play an essential role in quantum mechanics as they determine the time evolution of quantum states.
P. D. Hislop, I. M. Sigal
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SIAM Journal on Numerical Analysis, 2020
An implicit-explicit multistep method based on the backward difference formulae (BDF) is proposed for time discretization of parabolic equations with a non-self-adjoint operator.
Buyang Li, Kai Wang, Zhi Zhou
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An implicit-explicit multistep method based on the backward difference formulae (BDF) is proposed for time discretization of parabolic equations with a non-self-adjoint operator.
Buyang Li, Kai Wang, Zhi Zhou
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Mathematical Notes, 2005
Let \(A\) be an operator of the form \[ A\equiv JL= (\text{sgn\,}t)\Biggl(- {d^2\over dt^2} Q\Biggr), \] where \(\text{dom}(A)= \text{dom}(L)\). The main result in the paper is that the spectrum of the operator \(A\) is real, and \(A\) is similar to a selfadjoint operator if and only if \(Q\geq 0\).
Karabash, I. M., Hassi, S.
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Let \(A\) be an operator of the form \[ A\equiv JL= (\text{sgn\,}t)\Biggl(- {d^2\over dt^2} Q\Biggr), \] where \(\text{dom}(A)= \text{dom}(L)\). The main result in the paper is that the spectrum of the operator \(A\) is real, and \(A\) is similar to a selfadjoint operator if and only if \(Q\geq 0\).
Karabash, I. M., Hassi, S.
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Strongly Supercommuting Self-Adjoint Operators
Integral Equations and Operator Theory, 2004For unbounded self-adjoint operators, strong commutativity is defined in terms of commutativity of the corresponding spectral measures. In 1983, the reviewer introduced a concept of strong anticommutativity, also expressed in terms of spectral measures [see Rev. Roum. Math. Pures Appl. 28, 77--91 (1983; Zbl 0525.47017)].
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, 2007
.The Schur transformation for generalized Nevanlinna functions has been defined and applied in [2]. In this paper we discuss its relation to a basic interpolation problem and study its effect on the minimal self-adjoint operator (or relation) realization
D. Alpay +3 more
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.The Schur transformation for generalized Nevanlinna functions has been defined and applied in [2]. In this paper we discuss its relation to a basic interpolation problem and study its effect on the minimal self-adjoint operator (or relation) realization
D. Alpay +3 more
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2011
Of particular importance in operator theory are self-adjoint operators. To this end, we first recall the notion of the adjoint of a bounded linear operator A on a Hilbert space X. A linear operator B on X is said to be an adjoint of A if $$(Ax,y) = (x, By), \quad x,y \epsilon X.$$
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Of particular importance in operator theory are self-adjoint operators. To this end, we first recall the notion of the adjoint of a bounded linear operator A on a Hilbert space X. A linear operator B on X is said to be an adjoint of A if $$(Ax,y) = (x, By), \quad x,y \epsilon X.$$
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