3 citations · 4 across the 11 of their papers we have counts for
12 papers
The -resolvent estimates for the Spinor Dirac operator on manifolds with boundary conditions
Ivan Beschastnyi, Fabrizio Colombo, Simao Andrade Lucas +1
The aim of this paper is to show that the spectral theory based on the S-spectrum is particularly well suited for the Dirac operator on manifolds, even in cases where the operator…
Sub-Riemannian structures and non-transitive Cartan geometries via Lie groupoids
Ivan Beschastnyi, Francesco Cattafi, João Nuno Mestre
In this paper we discuss how to associate a suitable non-transitive version of a Cartan connection to sub-Riemannian manifolds of corank 1 (including contact and quasi-contact sub-…
The -resolvent estimates for the Dirac operator on hyperbolic and spherical spaces
Ivan Beschastnyi, Fabrizio Colombo, Simão Andrade Lucas +1
This seminal paper marks the beginning of our investigation into on the spectral theory based on -spectrum applied to the Dirac operator on manifolds. Specifically, we examine i…
Schrödinger operators with non-integer power-law potentials and Lie-Rinehart algebras
Ivan Beschastnyi, Catarina Carvalho, Victor Nistor +1
We study Schrödinger operators with potentials that have power-law growth (not necessarily polynomial) at 0 and at using methods of Lie theory (Lie-Rinehar…
Analysis on noncompact manifolds and Index Theory: Fredholm conditions and Pseudodifferential operators
Ivan Beschastnyi, Catarina Carvalho, Victor Nistor +1
We provide Fredholm conditions for compatible differential operators on certain Lie manifolds (that is, on certain possibly non-compact manifolds with nice ends). We discuss in mor…
Self-adjointness criteria and self-adjoint extensions of the Laplace-Beltrami operator on -Grushin manifolds
Ivan Beschastnyi, Hadrian Quan
The Grushin plane serves as one of the simplest examples of a sub-Riemannian manifold whose distribution is of non-constant rank. Despite the fact that the singular set where this…
Embedding the Grushin Cylinder in and Schroedinger evolution
Ivan Beschastnyi, Ugo Boscain, Daniele Cannarsa +1
We consider the evolution of a free quantum particle on the Grushin cylinder, under different type of quantizations. In particular we are interested to understand if the particle c…
Small-time local controllability of the bilinear Schrödinger equation, despite a quadratic obstruction, thanks to a cubic term
Mégane Bournissou
We consider a 1D linear Schr{ö}dinger equation, on a bounded interval, with Dirichlet boundary conditions and bilinear control. We study its controllability around the ground state…
Closure of the Laplace-Beltrami operator on 2D almost-Riemannian manifolds and semi-Fredholm properties of differential operators on Lie manifolds
Ivan Beschastnyi
The problem of determining the domain of the closure of the Laplace-Beltrami operator on a 2D almost-Riemannian manifold is considered. Using tools from theory of Lie groupoids nat…
Quantum confinement for the curvature Laplacian on 2D-almost-Riemannian manifolds
Ivan Beschastnyi, Ugo Boscain, Eugenio Pozzoli
Two-dimension almost-Riemannian structures of step 2 are natural generalizations of the Grushin plane. They are generalized Riemannian structures for which the vectors of a local o…
Cartan connections for stochastic developments on sub-Riemannian manifolds
Ivan Beschastnyi, Karen Habermann, Alexandr Medvedev
Analogous to the characterisation of Brownian motion on a Riemannian manifold as the development of Brownian motion on a Euclidean space, we construct sub-Riemannian diffusions on…
An obstruction to small-time controllability of the bilinear Schr{ö}dinger equation
Ivan Beschastnyi, Ugo Boscain, Mario Sigalotti
In this article we discuss which controllability properties of classical Hamiltonian systems are preserved after quantization. We discuss some necessary and some sufficient conditi…