607 citations
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6 papers · 2 filters
Global properties of vector fields on compact Lie groups in Komatsu classes. II. Normal forms
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Michael Ruzhansky
Let and be compact Lie groups, , and consider the operator \begin{equation*} L_{aq} = X_1 + a(x_1)X_2 + q(x_1,x_2), \en…
Global properties of vector fields on compact Lie groups in Komatsu classes
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Michael Ruzhansky
In this paper we characterize completely the global hypoellipticity and global solvability in the sense of Komatsu (of Roumieu and Beurling types) of constant-coefficients vector f…
Global hypoellipticity and global solvability for vector fields on compact Lie groups
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Michael Ruzhansky
We present necessary and sufficient conditions to have global hypoellipticity and global solvability for a class of vector fields defined on a product of compact Lie groups. In vie…
Partial Fourier series on compact Lie groups
Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Michael Ruzhansky
In this note we investigate the partial Fourier series on a product of two compact Lie groups. We give necessary and sufficient conditions for a sequence of partial Fourier coeffic…
Global hypoellipticity for a class of periodic Cauchy operators
Fernando de Ávila Silva
This note presents an investigation on the global hypoellipticity problem for Cauchy operators on belonging to the class \linebreak $L = \prod_{j=1}^{m}\left(D_t…
Global Hypoellipticity for Strongly Invariant Operators
Alexandre Kirilov, Wagner Augusto Almeida de Moraes
In this note, by analyzing the behavior at infinity of the matrix symbol of an invariant operator with respect to a fixed elliptic operator, we obtain a necessary and sufficien…