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Sandro Coriasco

Publications and source records attributed to Sandro Coriasco.

At least 19 recordsLinked to original sources
arXiv2026

Hypoellipticity on time-periodic space-times

We study the hypoellipticity of operators on a product type Lorentzian manifold where the time variable is periodic. In particular, we prove that hypoellipticity holds for such time-periodic equations, with a stronger estimate when the mass parameter or time period lies outside a set of arbitrarily small measure. We consider both compact and noncompact spatial manifolds and provide explicit examples involving the wave operator. The proof relies on a Fourier series decomposition and asymptotics for eigenvalue counting functions.

math.AP↗
arXiv2026

Top-Degree Global Solvability for Tube Complexes in Gevrey Ultradistributions

Let $s>1$, let $M$ be a connected, non-compact, oriented real-analytic manifold, and let $\omega_1,\ldots,\omega_m$ be real-valued closed $1$-forms of Gevrey order $s$ on $M$. We study the differential complex naturally associated with this family on $M\times\mathbb{T}^m$. We prove that its top-degree operator is globally solvable in Roumieu Gevrey ultradistributions, or equivalently that the corresponding top-degree cohomology vanishes. No global hypoellipticity assumption and no arithmetic condition on the periods of the defining forms are required. The proof is carried out in the physical variables and combines fiber translations, a local normal form, and a transport formula along paths in the base manifold. These tools yield propagation of Gevrey regularity, non-confinement of Gevrey singularities, and the support control needed to apply an abstract solvability criterion. The result highlights a sharp contrast with the compact setting, where compatibility conditions are unavoidable and solvability for compatible data may depend on exponential small-denominator conditions.

math.AP↗
arXiv2026

A parametrix construction for time-fractional partial differential equations

We prove in detail how to construct the parametrix of a parameter-dependent family of pseudodifferential operators, appearing in the analysis of time-fractional partial differential equations. In particular, we perform a precise study of the dependence from the parameter of the corresponding asymptotic expansion terms, as well as of the smoothing remainders. Moreover, we provide some results about the Laplace transform of vector-valued distributions, also appearing in the analysis of time-fractional partial differential equations.

math.AP↗
arXiv2026

Gelfand-Shilov spaces and operators with ultradifferential weighted symbols on non-compact manifolds

We invariantly define Gelfand-Shilov spaces on classes of non-compact manifolds with a certain ``structure at infinity''. We also construct and study a global calculus of pseudodifferential operators on such manifolds, locally defined by symbols satisfying estimates associated with weight sequences. The operators so obtained act naturally on the previously defined Gelfand-Shilov spaces. These generalise analogous functional spaces and operators defined on Euclidean spaces.

math.AP↗
arXiv2026

Global Gevrey Hypoellipticity of Involutive Systems on Non-Compact Manifolds

We investigate the global Gevrey hypoellipticity of a class of first-order differential operators associated with tube-type involutive structures on $M\times\mathbb{T}^m$, where $M$ is a non-compact manifold diffeomorphic to the interior of a compact manifold with boundary and $\mathbb{T}^m$ is the $m$-dimensional torus. For $s>1$, we work in Gevrey classes of Roumieu and Beurling type. A key step is the construction, on $M$, of a scattering metric whose coefficients are Gevrey of order $s$ in every analytic chart; this allows us to use Hodge theory and obtain Gevrey regularity for the harmonic forms. Under a natural condition on the defining closed $1$-forms, we obtain a sharp criterion for global Gevrey hypoellipticity in terms of rationality and (Roumieu/Beurling) exponential Liouville behavior.

math.AP↗
arXiv2025

Global Solvability for Involutive Systems on Non-Compact Manifolds

We establish necessary and sufficient conditions for the closedness of the range of a class of first-order differential operators associated with an involutive structure on $M\times\mathbb{T}^m$, where $M$ is a non-compact manifold satisfying suitable geometric assumptions and $\mathbb{T}^m$ is the $m$-dimensional torus. In addition, we prove that a weaker notion of global hypoellipticity ensures the closedness of the range for differential operators on smooth paracompact manifolds, thereby extending to the non-compact setting a result previously obtained by G.~Ara\'ujo, I.~Ferra, and L.~Ragognette [J. Anal. Math. 148, No. 1, 85-118, 2022] for compact manifolds.

math.AP↗
arXiv2025

Representation formula, regularity and decay of solutions for sub-diffusion type equations

We study regularity and decay properties for the solutions of the Cauchy problem for time-fractional partial differential equations, with tempered initial data, belonging to suitable (weighted) Sobolev spaces, associated with a differential operator on space variables with polynomially bounded coefficients. We obtain a representation formula for the solution, modulo time-regular functions, smooth and rapidly decreasing with respect to the space variables. By means of the representation formula, the (decay and smoothness) singularities of the solution of the homogeneous Cauchy problem can be controlled, in terms of (global) wavefront sets of the initial data.

math.AP↗
arXiv2025

Global hypoellipticity for involutive systems on non-compact manifolds

We study the global hypoellipticity of the operator $\mathbb{L} = \mathrm{d}_t + \sum_{k=1}^m \omega_k \wedge \partial_{x_k}$, defined on differential forms over product manifolds of the form $M \times \mathbb{T}^m$, where $M$ is a non-compact manifold homeomorphic to the interior of a compact manifold with boundary, equipped with a scattering metric, and $\omega_1,\dots,\omega_m$ are smooth closed 1-forms on $M$. Extending previous results obtained in the compact setting, we characterize global hypoellipticity of $\mathbb{L}$ in terms of arithmetic properties of the forms $\omega_k$. The analysis relies on microlocal techniques adapted to the scattering setting and a version of the Hodge Theorem for scattering manifolds.

math.AP↗
arXiv2025

Global hypoellipticity and solvability for a class of evolution operators in time-periodic weighted Sobolev spaces

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 introduce a class of time-periodic weighted Sobolev spaces, whose elements are characterised in terms of suitable Fourier expansions, associated with elliptic operators.

math.AP↗
arXiv2024

Quasi-Banach Schatten-von Neumann properties in Weyl-H\"ormander calculus

We study structural properties of Wiener-Lebesgue spaces with respect to a slowly varying metrics and certain Lebesgue parameters. For $p\in (0,1]$, we deduce Schatten-$p$ properties for pseudo-differential operators whose symbols, together with their derivatives, obey suitable Wiener-Lebesgue-boundedness conditions. Especially, we perform such investigations for the Weyl-H\"ormander calculus. Finally, we apply our results to global-type SG and Shubin pseudo-differential operators.

math.FA↗
arXiv2023

Chaos expansion solutions of a class of magnetic Schr\"odinger Wick-type stochastic equations on $\mathbb{R}^d$

We treat some classes of linear and semilinear stochastic partial differential equations of Schr\"odinger type on $\mathbb{R}^d$, involving a non-flat Laplacian, within the framework of white noise analysis, combined with Wiener-It\^o chaos expansions and pseudodifferential operator methods. The initial data and potential term of the Schr\"odinger operator are assumed to be generalized stochastic processes that have spatial dependence. We prove that the equations under consideration have unique solutions in the appropriate (intersections of weighted) Sobolev-Kato-Kondratiev spaces.

math.AP↗
arXiv2023

Fourier type operators on Orlicz spaces and the role of Orlicz Lebesgue exponents

We deduce continuity and (global) wave-front properties of classes of Fourier multipliers, pseudo-differential, and Fourier integral operators when acting on Orlicz spaces, or more generally, on Orlicz-Sobolev type spaces. In particular, we extend H{\"o}rmander's improvement of Mihlin's Fourier multiplier theorem to the framework of Orlicz spaces. We also show how Young functions $\Phi$ of the Orlicz spaces are linked to properties of certain Lebesgue exponents $p_\Phi$ and $q_\Phi$ emerged from $\Phi$.

math.FA↗
arXiv2023

Global Wellposedness of a Class of Weakly Hyperbolic Cauchy Problems with Variable Multiplicities on $\mathbb{R}^d$

We study a class of weakly hyperbolic Cauchy problems on $\mathbb{R}^d$, involving linear operators with characteristics of variable multiplicities, whose coefficients are unbounded in the space variable. The behaviour in the time variable is governed by a suitable "shape function". We develop a parameter-dependent symbolic calculus, corresponding to an appropriate subdivision of the phase space. By means of such calculus, a parametrix can be constructed, in terms of (generalized) Fourier integral operators naturally associated with the employed symbol class. Further, employing the parametrix, we prove $\mathscr{S}(\mathbb{R}^{d})$-wellposedness and give results about the global decay and regularity of the solution, within a scale of weighted Sobolev space.

math.AP↗
arXiv2022

Solution theory to semilinear stochastic equations of Schr\"odinger type on curved spaces I -- Operators with uniformly bounded coefficients

We study the Cauchy problem for Schr\"odinger type stochastic partial differential equations with uniformly bounded coefficients on a curved space. We give conditions on the coefficients, on the drift and diffusion terms, on the Cauchy data, and on the spectral measure associated with the noise, such that the Cauchy problem admits a unique function-valued mild solution in the sense of Da Prato and Zabczyc.

math.AP↗
arXiv2020

Solution theory to semilinear parabolic stochastic partial differential equations with polynomially bounded coefficients

We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide conditions on the initial data and on the stochastic terms, namely, on the associated spectral measure, so that these mild solutions exist uniquely in suitably chosen functional classes.

math.PR↗
arXiv2019

Weyl Law on Asymptotically Euclidean Manifolds

We study the asymptotic behaviour of the eigenvalue counting function for self-adjoint elliptic linear operators defined through classical weighted symbols of order $(1,1)$, on an asymptotically Euclidean manifold. We first prove a two term Weyl formula, improving previously known remainder estimates. Subsequently, we show that under a geometric assumption on the Hamiltonian flow at infinity there is a refined Weyl asymptotics with three terms. The proof of the theorem uses a careful analysis of the flow behaviour in the corner component of the boundary of the double compactification of the cotangent bundle. Finally, we illustrate the results by analysing the operator $Q=(1+|x|^2)(1-\Delta)$ on $\mathbb{R}^d$.

math.FA↗
arXiv2019

Bilinear pseudo-differential operators with Gevrey-H\"ormander symbols

We consider bilinear pseudo-differential operators whose symbols posses Gevrey type regularity and may have a sub-exponential growth at infinity, together with all their derivatives. It is proved that those symbol classes can be described by the means of the short-time Fourier transform and modulation spaces. Our first main result is the invariance property of the corresponding bilinear operators. Furthermore we prove the continuity of such operators when acting on modulation spaces. As a consequence, we derive their continuity on anisotropic Gelfand-Shilov type spaces. We consider both Beurling and Roumieu type symbol classes and Gelfand-Shilov spaces.

math.FA↗