Related papers: Perturbations of globally hypoelliptic operators o…
We show that an obstruction of number-theoretical nature appears as a necessary condition for the global hypoellipticity of the pseudo-differential operator $L=D_t+(a+ib)(t)P(D_x)$ on $\mathbb{T}^1_t\times\mathbb{T}_x^{N}$. This condition…
The paper is devoted to establishing relationships between global and local monotonicity, as well as their maximality versions, for single-valued and set-valued mappings between finite-dimensional and infinite-dimensional spaces. We first…
We study the Laplacian in deformed thin (bounded or unbounded) tubes in ?$\R^3$, i.e., tubular regions along a curve $r(s)$ whose cross sections are multiplied by an appropriate deformation function $h(s)> 0$. One the main requirements on…
This article offers a study of the Calder\'on type inverse problem of determining up to second order coefficients of the higher order elliptic operator. Here we show that it is possible to determine an anisotropic second order perturbation…
We use variational methods to derive Hadamard-type formulae for the eigenvalues of a class of elliptic operators on a compact Riemannian manifold $M$. We then apply the latter in the following context. Consider a family of elliptic…
In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…
In this paper we establish a hypoellipticity result for second order linear operators comprised by a linear combination, with infinite vanishing coefficients, of subelliptic operators in separate spaces. This generalizes previous known…
A differential operator $T$ satisfies the $L^2$-unique continuation property if every $L^2$-solution of $T$ that vanishes on an open subset vanishes identically. We study the $L^2$-unique continuation property of an operator $T$ acting on a…
In this paper we completely classify symplectic actions of a torus $T$ on a compact connected symplectic manifold $(M, \sigma)$ when some, hence every, principal orbit is a coisotropic submanifold of $(M, \sigma)$. That is, we construct an…
In this paper we establish that several maximal operators of convolution type, associated to elliptic and parabolic equations, are variation-diminishing. Our study considers maximal operators on the Euclidean space $\mathbb{R}^d$, on the…
The homogenization of elliptic divergence-type fourth-order operators with periodic coefficients is studied in a (periodic) domain. The aim is to find an operator with constant coefficients and represent the equation through a perturbation…
The techniques developed by Popescu, Muhly-Solel and Good for the study of algebras generated by weighted shifts are applied to generalize results of Sarkar and of Bhattacharjee-Eschmeier-Keshari-Sarkar concerning dilations and invariant…
We generalise the notion of the Pseudo-Laplacian on a hyperbolic Riemann surface with one cusp, that was studied by Lax and Phillips and Colin de Verdi\`ere, by considering a boundary condition of Robin type for the constant term instead of…
Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means…
In this paper, a sufficient condition for the existence of hyperinvariant subspace of compact perturbations of multiplication operators on some Banach spaces is presented. An interpretation of this result for compact perturbations of normal…
This is the final part of a series of papers where we study perturbations of divergence form second order elliptic operators $-\operatorname{div} A \nabla$ by first and zero order terms, whose complex coefficients lie in critical spaces,…
Structured perturbation results for invariant subspaces of $\Delta$-Hermitian and Hamiltonian matrices are provided. The invariant subspaces under consideration are associated with the eigenvalues perturbed from a single defective…
We consider a class of quasi-integrable Hamiltonian systems obtained by adding to a non-convex Hamiltonian function of an integrable system a perturbation depending only on the angle variables. We focus on a resonant maximal torus of the…
We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. This operator is perturbed by a first order differential operator, the coefficients of which depend arbitrarily on a…
Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$,…