Self-adjoint extensions and unitary operators on the boundary
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DOI: 10.1007/s11005-017-1001-8
Abstract: 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. Each unitary encodes a specific relation between the boundary value of… read more here.
Keywords: adjoint extensions; operators boundary; boundary self; unitary operators ... See more keywords
Fractional Sturm–Liouville Equations: Self-Adjoint Extensions
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DOI: 10.1007/s11785-018-0828-z
Abstract: 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 biological interpretation of the fractional order equation and nonlocal boundary conditions that… read more here.
Keywords: sturm liouville; liouville equations; sturm; fractional sturm ... See more keywords
Asymptotics of the Eigenvalues of Self-adjoint Fourth Order Boundary Value Problems
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DOI: 10.1007/s12591-021-00567-7
Abstract: A regular fourth order differential equation which depends quadratically on the eigenvalue parameter $$\lambda$$ is considered with classes of separable boundary conditions, where exactly one of the boundary conditions depends on $$\lambda$$ linearly. This problem… read more here.
Keywords: self adjoint; adjoint fourth; fourth order; eigenvalues self ... See more keywords
Eigenvalues of Fourth-Order Boundary Value Problems with Self-Adjoint Canonical Boundary Conditions
Sign Up to like & getrecommendations! Published in 2019 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-018-00714-4
Abstract: Fourth-order boundary value problems with general real self-adjoint boundary conditions are investigated. It is obtained that the eigenvalues of the problem depend not only continuously on all parameters of the problem but also smoothly on… read more here.
Keywords: order boundary; self adjoint; fourth order; boundary conditions ... See more keywords
On self-adjoint boundary conditions for singular Sturm–Liouville operators bounded from below
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2020.05.005
Abstract: We extend the classical boundary values \begin{align*} & g(a) = - W(u_{a}(\lambda_0,.), g)(a) = \lim_{x \downarrow a} \frac{g(x)}{\hat u_{a}(\lambda_0,x)}, \\ &g^{[1]}(a) = (p g')(a) = W(\hat u_{a}(\lambda_0,.), g)(a) = \lim_{x \downarrow a} \frac{g(x) - g(a)… read more here.
Keywords: liouville operators; sturm liouville; self adjoint; hat lambda ... See more keywords
Stability of direct and inverse scattering problems for the self-adjoint Schrödinger operators on the half-line
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125217
Abstract: Abstract The self-adjoint Schrodinger operators on the half-line with the real-valued potential are investigated. The estimates for the difference of the reflection coefficients are given by the differences of the corresponding potentials and the parameters… read more here.
Keywords: operators half; self adjoint; direct inverse; half line ... See more keywords
Operators commuting with self-adjoint weighted composition operators on H2
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DOI: 10.1080/17476933.2020.1804379
Abstract: In this paper we study weighted composition operators W g , ψ commuting with self-adjoint weighted composition operators W f , ϕ on the Hardy space H 2 . In particular, we investigate which combina... read more here.
Keywords: weighted composition; commuting self; composition operators; self adjoint ... See more keywords
On Oscillation Properties of Self-Adjoint Boundary Value Problems of Fourth Order
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DOI: 10.1134/s1064562421010166
Abstract: The connection between the number of internal zeros of nontrivial solutions to fourth-order self-adjoint boundary value problems and the inertia index of these problems is studied. We specify the types of problems for which such… read more here.
Keywords: self adjoint; adjoint boundary; fourth order; boundary value ... See more keywords
On 3D and 1D Weyl particles in a 1D box
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DOI: 10.1140/epjp/s13360-020-00820-y
Abstract: We construct the most general families of self-adjoint boundary conditions for three (equivalent) Weyl Hamiltonian operators, each describing a three-dimensional Weyl particle in a one-dimensional box situated along a Cartesian axis. These results are essentially… read more here.
Keywords: weyl; one dimensional; box; self adjoint ... See more keywords
Self-adjoint fourth order differential operators with eigenvalue parameter dependent and periodic boundary conditions
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DOI: 10.1186/s13661-017-0768-y
Abstract: Fourth order eigenvalue problems with periodic and separated boundary conditions are considered. One of the separated boundary conditions depends linearly on the eigenvalue parameter λ. These problems can be represented by an operator polynomial L(λ)=λ2M−iαλK−A$L(\lambda)=\lambda… read more here.
Keywords: boundary conditions; self adjoint; fourth order; eigenvalue parameter ... See more keywords
On some general inequalities related to operator AM-GM inequality
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DOI: 10.2298/fil2011601s
Abstract: Let B (H) be the C∗–algebra of all bounded linear operators on a Hilbert spaceH . As usual, we reserve m, M for scalars and I for the identity operator onH . A self adjoint… read more here.
Keywords: operator inequality; inequalities related; related operator; self adjoint ... See more keywords