43 citations · 106 across the 34 of their papers we have counts for
5 papers · 1 filter
Bounds and extremal domains for Robin eigenvalues with negative boundary parameter
Pedro R. S. Antunes, Pedro Freitas, David Krejcirik
We present some new bounds for the first Robin eigenvalue with a negative boundary parameter. These include the constant volume problem, where the bounds are based on the shrinking…
Summation formula inequalities for eigenvalues of the perturbed harmonic oscillator
Pedro Freitas, James B. Kennedy
We derive explicit inequalities for sums of eigenvalues of one-dimensional Schrödinger operators on the whole line. In the case of the perturbed harmonic oscillator, these bounds c…
Summation formula inequalities for eigenvalues of Schrödinger operators
Pedro Freitas, James B. Kennedy
We derive inequalities for sums of eigenvalues of Schrödinger operators on finite intervals and tori. In the first of these cases, the inequalities converge to the classical trace…
The spectrum of geodesic balls on spherically symmetric manifolds
Denis Borisov, Pedro Freitas
We study the Dirichlet spectrum of the Laplace operator on geodesic balls centred at a pole of spherically symmetric manifolds. We first derive a Hadamard--type formula for the dep…
A lower bound to the spectral threshold in curved quantum layers
Pedro Freitas, David Krejcirik
We derive a lower bound to the spectral threshold of the Dirichlet Laplacian in tubular neighbourhoods of constant radius about complete surfaces. This lower bound is given by the…