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+34 946 567 842
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+34 946 567 842
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lfanelli@bcamath.org
Information of interest
- Orcid: 0000-0003-1714-1611
BCAM-UPV/EHU Researcher.
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Non-existence of Radial Eigenfunctions for the Perturbed Heisenberg Sublaplacian
Fanelli, L.
; Mizutani, H.; Roncal, L.; Schiavone, N.M. (2025)
We prove uniform resolvent estimates in weighted L2-spaces for radial solutions of the sublaplacian on the Heisenberg group ℍd. The proofs are based on the multipliers methods, and strongly rely on the use of suitable ...
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A relativistic Hardy-type inequality with minimisers
Pizzichillo, F.; Fanelli, L. (2025)
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Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials
Fanelli, L.; Cossetti, L.; Krejcirik, D. (2024)
We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under which the spectrum remains stable. Our ...
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QUANTITATIVE HARDY INEQUALITY FOR MAGNETIC HAMILTONIANS
Fanelli, L.; Kovarík, H. (2024)
In this paper we present a new method of proof of Hardy type inequalities for two- dimensional quantum Hamiltonians with a magnetic field of finite flux. Our approach gives a quanti- tative lower bound on the best constant ...
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Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains
Fanelli, L.; Cossetti, L.; Alejo, M.A; Muñoz, C; Valenzuela, N (2024)
We consider the subcritical nonlinear Schrödinger (NLS) in dimension one posed on the unbounded real line. Several previous works have considered the deep neural network approximation of NLS solutions from the numerical ...
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Uniform resolvent estimates, smoothing effects and spectral stability for the Heisenberg sublaplacian
Fanelli, L.; Mizutani, H.; Roncal, L.; Schiavone, N.M. (2024)
We establish global bounds for solutions to stationary and time-dependent Schrödinger equations associated with the sublaplacian on the Heisenberg group, as well as its pure fractional power s and conformally invariant ...
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Intertwining operators beyond the Stark Effect
Fanelli, L.; Su, X.; Wang, Y.; Zhang, J.; Zheng, J. (2024)
The main mathematical manifestation of the Stark effect in quantum mechanics is the shift and the formation of clusters of eigenvalues when a spherical Hamiltonian is perturbed by lower order terms. Understanding this ...
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Unique continuation properties from one time for hyperbolic Schrödinger equations
Fanelli, L.; Barcelo, J.; Cassano, B. (2023)
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Kato–Ponce estimates for fractional sublaplacians in the Heisenberg group
Fanelli, L.; Roncal, L. (2022-11-04)
We give a proof of commutator estimates for fractional powers of the sublaplacian on the Heisenberg group. Our approach is based on pointwise and $L^p$ estimates involving square fractional integrals and Littlewood--Paley ...
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Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D
Fanelli, L.; Zhang, J.; Zheng, J. (2021)
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On the improvement of the Hardy inequality due to singular magnetic fields
Fanelli, L.; Krejčiřík, D.; Laptev, A.; Vega, L. (2020-09-01)
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ...
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On the improvement of the Hardy inequality due to singular magnetic fields
Fanelli, L.; Krejcirik, D.; Laptev, A.; Vega, L. (2018-07-12)
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ...
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On the improvement of the Hardy inequality due to singular magnetic fields
Fanelli, L.; Krejcirik, D.; Laptev, A.; Vega, L. (2018-07-12)
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ...
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Spectral stability of Schrödinger operators with subordinated complex potentials
Fanelli, L.; Krejcirik, D.; Vega, L. (2018-06-28)
We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing ...
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Absence of eigenvalues of two-dimensional magnetic Schroedinger operators
Fanelli, L.; Krejcirik, D.; Vega, L. (2018-01-01)
By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point ...
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Absence of eigenvalues of two-dimensional magnetic Schr ̈odinger operators
Fanelli, L.; Krejcirik, D.; Vega, L. (2017-10-17)
By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schr ̈odinger operator possesses no point ...
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Gaussian Decay of Harmonic Oscillators and related models
Cassano, B.; Fanelli, L. (2017-05-15)
We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ...
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Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866-876, DOI 10.1007/s10955-014-0915-0]
Fanelli, L.; Vega, L.; Visciglia, N. (2015-12-31)
[No abstract available]
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Relativistic Hardy Inequalities in Magnetic Fields
Fanelli, L.; Vega, L.; Visciglia, N. (2014-12-31)
We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality ...