18 citations · 40 across the 9 of their papers we have counts for
10 papers
Dirac operators on periodic planar graphs: the right definition advocated by flat bands
Koichi Kato, Daniel Parra, Serge Richard
Massive discrete Dirac-type operators on periodic planar graphs are investigated. Using Floquet--Bloch decomposition, we first show that neglecting the faces leads to spurious flat…
Eigenvalue Asymptotics near a flat band in presence of a slowly decaying potential
Pablo Miranda, Daniel Parra
We provide eigenvalue asymptotics for a Dirac-type operator on , , perturbed by multiplication operators that decay as with . We show that the…
Continuum limit for a discrete Hodge-Dirac operator on square lattices
Pablo Miranda, Daniel Parra
We study the continuum limit for Dirac-Hodge operators defined on the dimensional square lattice as goes to . This result extends to a first order discre…
Spectral Asymptotics at Thresholds for a Dirac-type Operator on
Pablo Miranda, Daniel Parra, Georgi Raikov
In this article, we provide the spectral analysis of a Dirac-type operator on by describing the behavior of the spectral shift function associated with a sign-defini…
Eigenvalue and Resonance Asymptotics in perturbed periodically twisted tubes: Twisting versus Bending
Vincent Bruneau, Pablo Miranda, Daniel Parra +1
We consider the Dirichlet Laplacian in a three-dimensional waveguide that is a small deformation of a periodically twisted tube. The deformation is given by a bending and an additi…
Does Levinson's theorem count complex eigenvalues ?
F. Nicoleau, D. Parra, S. Richard
Yes it does ! Indeed an extended version of Levinson's theorem is proposed for a system involving complex eigenvalues. The perturbed system corresponds to a realization of the Schr…
Spectral and scattering theory for Gauss-Bonnet operators on perturbed topological crystals
Daniel Parra
In this paper we investigate the spectral and the scattering theory of Gauss--Bonnet operators acting on perturbed periodic combinatorial graphs. Two types of perturbation are cons…
Spectral and scattering theory for Schrödinger operators on perturbed topological crystals
Daniel Parra, Serge Richard
In this paper we investigate the spectral and the scattering theory of Schrödinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two t…
Continuity of the spectra for families of magnetic operators on Z^d
D. Parra, S. Richard
For families of magnetic self-adjoint operators on whose symbols and magnetic fields depend continuously on a parameter , it is shown that the main spectral prop…
Compactness Criteria for Sets and Operators in the Setting of Continuous Frames
M. Mantoiu, D. Parra
To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting sp…