Abstract
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 ultradif-ferentiable classes defined via weight matrices. In particular, our results simultaneously apply to the two standard classes defined via weight sequences and via weight functions.
| Original language | English |
|---|---|
| Number of pages | 30 |
| Journal | Publications of the Research Institute for Mathematical Sciences |
| Issue number | 3 |
| Publication status | Published - 2023 |
Bibliographical note
Publisher Copyright:© 2023 Research Institute for Mathematical Sciences, Kyoto University.