Quasianalytic functionals and ultradistributions as boundary values of harmonic functions
We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to Hörmander’s support theorem for quasianalytic functionals. Our main technical tool is a description of ult...
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| creator | Debrouwere, Andreas Vindas Diaz, Jasson |
| description | We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to Hörmander’s support theorem for quasianalytic functionals. Our main technical tool is a description of ultradifferentiable functions by almost harmonic functions, a concept that we introduce in this article. We work in the setting of ultradifferentiable classes defined via weight matrices. In particular, our results simultaneously apply to the two standard classes defined via weight sequences and via weight functions. |
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| source | Ghent University Academic Bibliography |
| subjects | almost harmonic functions boundary values boundary values of harmonic functions harmonic functions hyperfunctions Hörmander’s support theorem Mathematics and Statistics quasianalytic functionals ultradifferentiable classes ultradistributions |
| title | Quasianalytic functionals and ultradistributions as boundary values of harmonic functions |
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