10 citations · 30 across the 31 of their papers we have counts for
36 papers
Differential Complexes in Time-Periodic Gelfand-Shilov Spaces
Fernando de Ávila Silva, Marco Cappiello, Alexandre Kirilov +1
We study the global solvability of a class of differential complexes on the product manifold associated with systems of evolution operators of th…
The Cauchy problem for -evolution equations with initial data in Gelfand-Shilov spaces
Marco Cappiello, Eliakim Cleyton Machado
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 assumpti…
Smoothing effect for higher order dispersive equations and applications to nonlinear initial value problems
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
In this paper we deal with the initial value problem related to a family of dispersive inhomogeneous evolution equations Pu=f with variable coefficients belonging to the class of p…
Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces
Fernando de Ávila Silva, Marco Cappiello, Alexandre Kirilov
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-…
Schwartz very weak solutions for Schrödinger type equations with distributional coefficients
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello +1
This paper continues the analysis of Schrödinger type equations with distributional coefficients initiated by the authors in [3]. Here we consider coefficients that are tempered di…
The Cauchy problem for -evolution equations with variable coefficients in Gevrey classes
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello +1
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 assumpti…
Propagation of singularities for anharmonic Schrödinger equations
Marco Cappiello, Luigi Rodino, Patrik Wahlberg
We consider evolution equations for two classes of generalized anharmonic oscillators and the associated initial value problem in the space of tempered distributions. We prove that…
Systems of differential operators in time-periodic Gelfand-Shilov spaces
Fernando de Ávila Silva, Marco Cappiello, Alexandre Kirilov
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…
Globally solvable time-periodic evolution equations in Gelfand-Shilov classes
Fernando de Ávila Silva, Marco Cappiello
In this paper we consider a class of evolution operators with coefficients depending on time and space variables , where is t…
Schrödinger type equations with singular coefficients and lower order terms
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello +1
In this paper we investigate the well-posedness of the Cauchy problem for a Schrödinger operator with singular lower order terms. We allow distributional coefficients and we approa…
On the Cauchy problem for -evolution equations with variable coefficients: a necessary condition for Gevrey well-posedness
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
In this paper we consider a class of -evolution equations of arbitrary order with variable coefficients depending on time and space variables . We prove necessary conditi…
Propagation of anisotropic Gabor singularities for Schrödinger type equations
Marco Cappiello, Luigi Rodino, Patrik Wahlberg
We show results on propagation of anisotropic Gabor wave front sets for solutions to a class of evolution equations of Schrödinger type. The Hamiltonian is assumed to have a real-v…
KdV-type equations in projective Gevrey classes
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
We prove well-posedness of the Cauchy problem for a class of third order quasilinear evolution equations with variable coefficients in projective Gevrey spaces. The class considere…
Time-periodic Gelfand-Shilov spaces and global hypoellipticity on
Fernando de Ávila Silva, Marco Cappiello
We introduce a class of time-periodic Gelfand-Shilov spaces of functions on , where is the one-dimensiona…
Gevrey well posedness for -evolution equations with variable coefficients
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
We study the Cauchy problem for a class of third order linear anisotropic evolution equations with complex valued lower order terms depending both on time and space variables. Unde…
The Cauchy problem for -evolution equations with data in Gelfand-Shilov spaces
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
We consider the Cauchy problem for a -evolution operator with -depending coefficients and complex valued lower order terms. We assume the initial data to be Gevrey re…
Schrödinger-type equations in Gelfand-Shilov spaces
Alessia scanelli, Marco Cappiello
We study the initial value problem for Schrödinger-type equations with initial data presenting a certain Gevrey regularity and an exponential behavior at infinity. We assume the lo…
Pseudo-differential calculus in anisotropic Gelfand-Shilov setting
Ahmed Abdeljawad, Marco Cappiello, Joachim Toft
We study some classes of pseudo-differential operators with symbols admitting anisotropic exponential growth at infinity and we prove mapping properties for these operators on…
Shubin type Fourier integral operators and evolution equations
Marco Cappiello, René Schulz, Patrik Wahlberg
We study the Cauchy problem for an evolution equation of Schrödinger type. The Hamiltonian is the Weyl quantization of a real homogeneous quadratic form with a pseudodifferential p…
Lagrangian distributions and Fourier integral operators with quadratic phase functions and Shubin amplitudes
Marco Cappiello, René Schulz, Patrik Wahlberg
We study Fourier integral operators with Shubin amplitudes and quadratic phase functions associated to twisted graph Lagrangians with respect to symplectic matrices. We factorize s…
Conormal distributions in the Shubin calculus of pseudodifferential operators
Marco Cappiello, René Schulz, Patrik Wahlberg
We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of an FBI transform. Based on this we introduce as a generalization a new class of temp…
Anisotropic Shubin operators and eigenfunctions expansions in Gelfand-Shilov spaces
Marco Cappiello, Todor Gramchev, Stevan Pilipovic +1
We derive new results on the characterization of Gelfand--Shilov spaces , , by Gevrey estimates of the norms of iterates of …
Pseudo-differential operators in a Gelfand-Shilov setting
Marco Cappiello, Joachim Toft
We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on…
Pointwise decay and smoothness for semilinear elliptic equations and travelling waves
Marco Cappiello, Fabio Nicola
We derive sharp decay estimates and prove holomorphic extensions for the solutions of a class of semilinear nonlocal elliptic equations with linear part given by a sum of Fourier m…