28 citations · 68 across the 8 of their papers we have counts for
10 papers
The complexity of smooth words over binary alphabets
Julien Cassaigne, Raphaël Henry
Smooth sequences over an alphabet of positive integers are sequences that are infinitely derivable, the emblematic example being the Oldenburger-Kolakoski sequence ov…
On the minimal components of substitution subshifts
Raphaël Henry
In this paper we study substitutions on where is a finite alphabet. We precisely characterize the minimal components of substitution subshifts, give an optimal b…
Morphic Sequences: Complexity and Decidability
Raphael Henry
In this work we recall Pansiot's result on the complexity of pure morphic sequences and we use the tools developed by Devyatov for morphic sequences to prove the decidability of th…
The complex Airy operator with a semi-permeable barrier
D. S. Grebenkov, B. Helffer, R. Henry
We consider a suitable extension of the complex Airy operator, , on the real line with a transmission boundary condition at the origin. We provide a rigorous defini…
Spectral analysis of a complex Schrödinger operator in the semiclassical limit
Yaniv Almog, Raphaël Henry
We consider the Dirichlet realization of the operator in the semi-classical limit , where is a smooth real potential with no critical points. For a one dimens…
Pseudospectra of the Schroedinger operator with a discontinuous complex potential
Raphael Henry, David Krejcirik
We study spectral properties of the Schroedinger operator with an imaginary sign potential on the real line. By constructing the resolvent kernel, we show that the pseudospectra of…
On the semi-classical analysis of Schrödinger operators with purely imaginary electric potentials in a bounded domain
Raphaël Henry
In this paper, we describe the leftmost eigenvalue of the non-selfadjoint operator with Dirichlet boundary conditions on a smooth bounded domain $Ω\su…
Spectral projections of the complex cubic oscillator
Raphaël Henry
We prove the spectral instability of the complex cubic oscillator for non-negative values of the parameter , by getting the exponential growth rate…
Spectral instability of some non-selfadjoint anharmonic oscillators
Raphaël Henry
The purpose of this Note is to highlight the spectral instability of some non-selfadjoint differential operators, by studying the growth rate of the norms of the spectral projectio…
Spectral instability for even non-selfadjoint anharmonic oscillators
Raphaël Henry
We study the instability of the spectrum for a class of non-selfadjoint anharmonic oscillators, estimating the behavior of the instability indices (i. e. the norm of spectral proje…