110 citations · 425 across the 34 of their papers we have counts for
35 papers
A fresh look at the Peierls-Onsager substitution
Horia D. Cornean, Bernard Helffer, Radu Purice
We formulate a general version of the Peierls-Onsager substitution for a finite family of Bloch eigenvalues under a local spectral gap hypothesis, via strongly localized tight-fram…
The fibre operators in the Bloch-Floquet decomposition of periodic magnetic pseudo-differential operators
Horia D. Cornean, Bernard Helffer, Radu Purice
We study the structure of the fibre operators corresponding to periodic magnetic pseudo-differential operators having periodic magnetic potentials. We obtain explicit formulas for…
Spectral regularity with respect to dilations for a class of pseudodifferential operators
Horia D. Cornean, Radu Purice
We continue the study of the perturbation problem discussed in \cite{CP3} and get rid of the 'slow variation' assumption by considering symbols of the form …
A rigorous Peierls-Onsager effective dynamics for semimetals in long-range magnetic fields
Horia D. Cornean, Bernard Helffer, Radu Purice
We consider periodic (pseudo)differential {elliptic operators of Schrödinger type} perturbed by weak magnetic fields not vanishing at infinity, and extend our previous analysis in…
Sharp spectral stability for a class of singularly perturbed pseudo-differential operators
Horia D. Cornean, Radu Purice
Let be a real Hörmander symbol of the type , let be a smooth function with all its derivatives globally bounded, and let…
Matrix representation of Magnetic pseudo-differential operators via tight Gabor frames
Horia D. Cornean, Bernard Helffer, Radu Purice
In this paper we use some ideas from \cite{FG-97, G-06} and consider the description of Hörmander type pseudo-differential operators on (), including the cas…