18 citations · 26 across the 13 of their papers we have counts for
14 papers
Observability estimates for the Schrödinger equation on the equilateral triangle
Paul Alphonse, David Lafontaine
We prove observability estimates for the Schrödinger equation posed on the equilateral triangle in the plane, under both Neumann and Dirichlet boundary conditions. No geometric con…
Unique continuation estimates for Baouendi--Grushin equations on cylinders
Paul Alphonse, Albrecht Seelmann
We prove time-pointwise quantitative unique continuation estimates for the evolution operators associated to (fractional powers of) the Baouendi--Grushin operators on the cylinder…
Null-controllability for weakly dissipative heat-like equations
Paul Alphonse, Armand Koenig
We study the null-controllability properties of heat-like equations posed on the whole Euclidean space . These evolution equations are associated with Fourier multipli…
Null-controllability for weakly dissipative heat-like equations
Armand Koenig, Paul Alphonse
We study the null-controllability properties of heat-like equations posed on the whole Euclidean space . These evolution equations are associated with Fourier multipli…
Quantitative spectral inequalities for the anisotropic Shubin operators and applications to null-controllability
Paul Alphonse, Albrecht Seelmann
We prove quantitative spectral inequalities for the (anisotropic) Shubin operators on the whole Euclidean space, thus relating for functions from spectral subspaces associated to f…
Approximate null-controllability with uniform cost for the hypoelliptic Ornstein-Uhlenbeck equations
Paul Alphonse, Jérémy Martin
We prove that the approximate null-controllability with uniform cost of the hypoelliptic Ornstein-Uhlenbeck equations posed on is characterized by an integral thickne…
Gains of integrability and local smoothing effects for quadratic evolution equations
Paul Alphonse, Joackim Bernier
We characterize geometrically the semigroups generated by non-selfadjoint quadratic differential operators enjoying local smoothing effects and providing ga…
Stabilization and approximate null-controllability for a large class of diffusive equations from thick control supports
Paul Alphonse, Jérémy Martin
We prove that the thickness property is a necessary and sufficient geometric condition that ensures the (rapid) stabilization or the approximate null-controllability with uniform c…
Null-controllability of evolution equations associated with fractional Shubin operators through quantitative Agmon estimates
Paul Alphonse
We consider the anisotropic Shubin operators acting on the space , with some positive integers. We provide sharp quantit…
Hypoelliptic estimates for linear transport operators
Paul Alphonse
We aim at understanding how the non-commutation phenomena between a linear transport operator and a fractional diffusion allow the transport operator to satisfy hypoelliptic estima…
Description of the smoothing effects of semigroups generated by fractional Ornstein-Uhlenbeck operators and subelliptic estimates
Paul Alphonse
We study semigroups generated by general fractional Ornstein-Uhlenbeck operators acting on . We characterize geometrically the partial Gevrey-type smoothing proper…
Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects
Paul Alphonse, Joackim Bernier
We characterize geometrically the regularizing effects of the semigroups generated by accretive non-selfadjoint quadratic differential operators. As a byproduct, we establish the s…
Quadratic differential equations : partial Gelfand-Shilov smoothing effect and null-controllability
Paul Alphonse
We study the partial Gelfand-Shilov regularizing effect and the exponential decay for the solutions to evolution equations associated to a class of accretive non-selfadjoint quadra…
Smoothing Properties of Fractional Ornstein-Uhlenbeck Semigroups and Null-Controllability
Paul Alphonse, Joackim Bernier
We study fractional hypoelliptic Ornstein-Uhlenbeck operators acting on satisfying the Kalman rank condition. We prove that the semigroups generated by these op…