All Outputs (16)

Improved Lieb-Thirring type inequalities for non-selfadjoint Schroedinger operators (2023)
Book Chapter
Boegli, S. (2023). Improved Lieb-Thirring type inequalities for non-selfadjoint Schroedinger operators. In M. Brown, F. Gesztesy, P. Kurasov, A. Laptev, B. Simon, G. Stolz, & I. Wood (Eds.), From Complex Analysis to Operator Theory: A Panorama In Memory of Sergey Naboko (151-161). (1). Birkhaeuser-Springer. https://doi.org/10.1007/978-3-031-31139-0_9

We improve the Lieb–Thirring type inequalities by Demuth, Hansmann and Katriel (J. Funct. Anal. 2009) for Schr¨odinger operators with complex-valued potentials. Our result involves a positive, integrable function. We show that in the one-dimensional... Read More about Improved Lieb-Thirring type inequalities for non-selfadjoint Schroedinger operators.

On the asymptotic behavior of solutions to a class of grand canonical master equations (2023)
Journal Article
Vuillermot, P., & Bögli, S. (2023). On the asymptotic behavior of solutions to a class of grand canonical master equations. Portugaliae Mathematica, 80(3), 269-289. https://doi.org/10.4171/pm/2102

In this article, we investigate the long-time behavior of solutions to a class of infinitely many master equations defined from transition rates that are suitable for the description of a quantum system approaching thermodynamical equilibrium with a... Read More about On the asymptotic behavior of solutions to a class of grand canonical master equations.

Counterexample to the Laptev-Safronov Conjecture (2022)
Journal Article
Boegli, S., & Cuenin, J. (2023). Counterexample to the Laptev-Safronov Conjecture. Communications in Mathematical Physics, 398(3), 1349-1370. https://doi.org/10.1007/s00220-022-04546-z

Laptev and Safronov (Commun Math Phys 292(1):29–54, 2009) conjectured an inequality between the magnitude of eigenvalues of a non-self-adjoint Schrödinger operator on Rd, d≥2, and an Lq norm of the potential, for any q∈[d/2,d]. Frank (Bull Lond Math... Read More about Counterexample to the Laptev-Safronov Conjecture.

A Spectral Theorem for the Semigroup Generated by a Class of Infinitely Many Master Equations (2022)
Journal Article
Boegli, S., & Vuillermot, P. (2022). A Spectral Theorem for the Semigroup Generated by a Class of Infinitely Many Master Equations. Acta Applicandae Mathematicae, 178(1), Article 4. https://doi.org/10.1007/s10440-022-00478-x

In this article we investigate the spectral properties of the infinitesimal generator of an infinite system of master equations arising in the analysis of the approach to equilibrium in statistical mechanics. The system under consideration thus consi... Read More about A Spectral Theorem for the Semigroup Generated by a Class of Infinitely Many Master Equations.

On the eigenvalues of the Robin Laplacian with a complex parameter (2022)
Journal Article
Boegli, S., Kennedy, J. B., & Lang, R. (2022). On the eigenvalues of the Robin Laplacian with a complex parameter. Analysis and Mathematical Physics, 12(1), Article 39. https://doi.org/10.1007/s13324-022-00646-0

We study the spectrum of the Robin Laplacian with a complex Robin parameter α on a bounded Lipschitz domain Ω. We start by establishing a number of properties of the corresponding operator, such as generation properties, analytic dependence of the ei... Read More about On the eigenvalues of the Robin Laplacian with a complex parameter.

Spectral analysis and domain truncation for Maxwell's equations (2022)
Journal Article
Bögli, S., Ferraresso, F., Marletta, M., & Tretter, C. (2023). Spectral analysis and domain truncation for Maxwell's equations. Journal de Mathématiques Pures et Appliquées, 170, 96-135. https://doi.org/10.1016/j.matpur.2022.12.004

We analyse how the spectrum of the anisotropic Maxwell system with bounded conductivity σ on a Lipschitz domain Ω is approximated by domain truncation. First we prove a new non-convex enclosure for the spectrum of the Maxwell system, with weak assump... Read More about Spectral analysis and domain truncation for Maxwell's equations.

On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators (2021)
Journal Article
Boegli, S., & Stampach, F. (2021). On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators. Journal of Spectral Theory, 11(3), 1391-1413. https://doi.org/10.4171/jst/378

We study to what extent Lieb–Thirring inequalities are extendable from self-adjoint to general (possibly non-self-adjoint) Jacobi and Schrödinger operators. Namely, we prove the conjecture of Hansmann and Katriel from [12] and answer another open que... Read More about On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators.

Eigenvalues of Magnetohydrodynamic Mean-Field Dynamo Models: Bounds and Reliable Computation (2020)
Journal Article
Boegli, S., & Tretter, C. (2020). Eigenvalues of Magnetohydrodynamic Mean-Field Dynamo Models: Bounds and Reliable Computation. SIAM Journal on Applied Mathematics, 80(5), 2194-2225. https://doi.org/10.1137/19m1286359

This paper provides the first comprehensive study of the linear stability of three important magnetohydrodynamic (MHD) mean-field dynamo models in astrophysics, the spherically symmetric $\alpha^2$-model, the $\alpha^2\omega$-model, and the $\alpha\o... Read More about Eigenvalues of Magnetohydrodynamic Mean-Field Dynamo Models: Bounds and Reliable Computation.

The essential numerical range for unbounded linear operators (2020)
Journal Article
Bögli, S., Marletta, M., & Tretter, C. (2020). The essential numerical range for unbounded linear operators. Journal of Functional Analysis, 279(1), Article 108509. https://doi.org/10.1016/j.jfa.2020.108509

We introduce the concept of essential numerical range for unbounded Hilbert space operators T and study its fundamental properties including possible equivalent characterizations and perturbation results. Many of the properties known for the bounded... Read More about The essential numerical range for unbounded linear operators.

Essential numerical ranges for linear operator pencils (2019)
Journal Article
Boegli, S., & Marletta, M. (2020). Essential numerical ranges for linear operator pencils. IMA Journal of Numerical Analysis, 40(4), 2256-2308. https://doi.org/10.1093/imanum/drz049

We introduce concepts of essential numerical range for the linear operator pencil λ↦A−λB⁠. In contrast to the operator essential numerical range, the pencil essential numerical ranges are, in general, neither convex nor even connected. The new concep... Read More about Essential numerical ranges for linear operator pencils.

Local convergence of spectra and pseudospectra (2018)
Journal Article
Boegli, S. (2018). Local convergence of spectra and pseudospectra. Journal of Spectral Theory, 8(3), 1051-1098. https://doi.org/10.4171/jst/222

We prove local convergence results for the spectra and pseudospectra of sequences of linear operators acting in different Hilbert spaces and converging in generalised strong resolvent sense to an operator with possibly non-empty essential spectrum. W... Read More about Local convergence of spectra and pseudospectra.

Approximations of spectra of Schrödinger operators with complex potentials on ℝ^d (2017)
Journal Article
Boegli, S., Siegl, P., & Tretter, C. (2017). Approximations of spectra of Schrödinger operators with complex potentials on ℝ^d. Communications in Partial Differential Equations, 42(7), 1001-1041. https://doi.org/10.1080/03605302.2017.1330342

We study spectral approximations of Schrödinger operators T = −Δ+Q with complex potentials on Ω = ℝd, or exterior domains Ω⊂ℝd, by domain truncation. Our weak assumptions cover wide classes of potentials Q for which T has discrete spectrum, of approx... Read More about Approximations of spectra of Schrödinger operators with complex potentials on ℝ^d.

Convergence of Sequences of Linear Operators and Their Spectra (2017)
Journal Article
Boegli, S. (2017). Convergence of Sequences of Linear Operators and Their Spectra. Integral Equations and Operator Theory, 88(4), 559-599. https://doi.org/10.1007/s00020-017-2389-3

We establish spectral convergence results of approximations of unbounded non-selfadjoint linear operators with compact resolvents by operators that converge in generalized strong resolvent sense. The aim is to establish general assumptions that ensur... Read More about Convergence of Sequences of Linear Operators and Their Spectra.

Schrödinger Operator with Non-Zero Accumulation Points of Complex Eigenvalues (2016)
Journal Article
Boegli, S. (2017). Schrödinger Operator with Non-Zero Accumulation Points of Complex Eigenvalues. Communications in Mathematical Physics, 352(2), 629-639. https://doi.org/10.1007/s00220-016-2806-5

We study Schrödinger operators H=−Δ+V in L2(Ω) where Ω is Rd or the half-space Rd+, subject to (real) Robin boundary conditions in the latter case. For p>d we construct a non-real potential V∈Lp(Ω)∩L∞(Ω) that decays at infinity so that H has infinite... Read More about Schrödinger Operator with Non-Zero Accumulation Points of Complex Eigenvalues.

Guaranteed resonance enclosures and exclosures for atoms and molecules (2014)
Journal Article
Boegli, S., Brown, B. M., Marletta, M., Tretter, C., & Wagenhofer, M. (2014). Guaranteed resonance enclosures and exclosures for atoms and molecules. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470(2171), https://doi.org/10.1098/rspa.2014.0488

In this paper, we confirm, with absolute certainty, a conjecture on a certain oscillatory behaviour of higher auto-ionizing resonances of atoms and molecules beyond a threshold. These results not only definitely settle a more than 30 year old controv... Read More about Guaranteed resonance enclosures and exclosures for atoms and molecules.

Remarks on the Convergence of Pseudospectra (2014)
Journal Article
Boegli, S., & Siegl, P. (2014). Remarks on the Convergence of Pseudospectra. Integral Equations and Operator Theory, 80(3), 303-321. https://doi.org/10.1007/s00020-014-2178-1

We establish the convergence of pseudospectra in Hausdorff distance for closed operators acting in different Hilbert spaces and converging in the generalised norm resolvent sense. As an assumption, we exclude the case that the limiting operator has c... Read More about Remarks on the Convergence of Pseudospectra.