Globally hypoelliptic triangularizable systems of periodic pseudo-differential operators |
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Authors: | Fernando de Ávila Silva |
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Institution: | Departamento de Matemática, Universidade Federal do Paraná, Paraná, Brazil |
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Abstract: | This paper presents an investigation on the global hypoellipticity problem for a class of systems of pseudo-differential operators on the torus. The approach consists in establishing conditions on the matrix symbol of the system such that it can be transformed into a suitable triangular form involving a nilpotent upper triangular matrix. Hence, the global hypoellipticity is studied by analyzing the behavior of the eigenvalues and their averages. |
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Keywords: | Fourier series global hypoellipticity pseudo-differential operators triangularization |
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