Related papers: Globally solvable time-periodic evolution equation…
We introduce a class of time-periodic Gelfand-Shilov spaces of functions on $\mathbb{T} \times \mathbb{R}^n$, where $\mathbb{T} \sim \mathbb{R} /2\pi \mathbb{Z}$ is the one-dimensional torus. We develop a Fourier analysis inspired by the…
We study the global solvability of a class of differential complexes on the product manifold $\mathbb{T}^m \times \mathbb{R}^n$ associated with systems of evolution operators of the form $L_r = \partial_{t_r} + ia_r(t)P(x,D_x),…
This paper explores the global properties of time-independent systems of operators in the framework of Gelfand-Shilov spaces. Our main results provide both necessary and sufficient conditions for global solvability and global…
We study the hypoellipticity and solvability properties of a class of time-periodic evolution operators, with coefficients globally defined on $\mathbb{R}^d$ and growing polynomially with respect to the space variable. To this aim, we…
We introduce time-periodic Gevrey-Sobolev-Kato spaces on asymptotically Euclidean manifolds and study their characterisation throughout Fourier expansions associated with suitable elliptic operators. As an application, we study the global…
In this paper, we study the global properties of a class of evolution-like differential operator with a 0-order perturbation defined on the product of $r+1$ tori and $s$ spheres $\mathbb{T}^{r+1}\times(\mathbb{S}^{3})^s$, with $r$ and $s$…
In this paper, we provide a characterization of the time-periodic Gelfand-Shilov spaces, as introduced by F. de \'Avila Silva and M. Cappiello [J. Funct. Anal., 282(9):29, 2022], through the asymptotic behaviour of both the Euclidean and…
We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-Shilov spaces. Our main result provides necessary and…
In this paper we consider time dependent Schr\"odinger equations on the one-dimensional torus $\T := \R /(2 \pi \Z)$ of the form $\partial_t u = \ii {\cal V}(t)[u]$ where ${\cal V}(t)$ is a time dependent, self-adjoint pseudo-differential…
We consider evolution operators $G(t,s)$ associated to a class of nonautonomous elliptic operators with unbounded coefficients, in the space of bounded and continuous functions over $\mathbb{R}^d$. We prove some new pointwise estimates for…
We prove that a family of linear bounded evolution operators $({\bf G}(t,s))_{t\ge s\in I}$ can be associated, in the space of vector-valued bounded and continuous functions, to a class of systems of elliptic operators $\bm{\mathcal A}$…
In this paper we consider time dependent Schr{\"o}dinger linear PDEs of the form i$\partial$t$\psi$ = L(t)$\psi$, where L(t) is a continuous family of self-adjoint operators. We give conditions for well-posedness and polynomial growth for…
We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumptions on the coefficients of the lower order terms for $|x|$…
We consider the Cauchy problem for a $3$-evolution operator $P$ with $(t,x)$-depending coefficients and complex valued lower order terms. We assume the initial data to be Gevrey regular and to admit an exponential decay at infinity, that…
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest…
In this paper we prove a theorem of global time-extension for the local classical solution of Navier-Stokes's evolution problem in $\Real^n$ with $n\geqslant2$ for incompressible fluids subjected to external forces and regular initial…
We give a complete characterization for the global solvability of a pseudodifferential operator P=D_t + c(t,D_x) on the (N+1)-dimensional torus T^{N+1} = S^1_t x T^N_x. Our characterization is given in terms of diophantine conditions and a…
In this paper we consider nonautonomous elliptic operators ${\mathcal A}$ with nontrivial potential term defined in $I\times\mathbb R^d$, where $I$ is a right-halfline (possibly $I=\mathbb R$). We prove that we can associate an evolution…
In this paper we consider a class of $p$-evolution equations of arbitrary order with variable coefficients depending on time and space variables $(t,x)$. We prove necessary conditions on the decay rates of the coefficients for the…
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 quadratic operators, which fail to be globally hypoelliptic on the…