Pseudodifferential operators with generalized symbols and regularity theory
dc.contributor.author | Garetto, Claudia | |
dc.contributor.author | Gramchev, Todor | |
dc.contributor.author | Oberguggenberger, Michael | |
dc.date.accessioned | 2021-06-22T17:14:26Z | |
dc.date.available | 2021-06-22T17:14:26Z | |
dc.date.issued | 2005-10-21 | |
dc.description.abstract | We study pseudodifferential operators with amplitudes ɑε(x, ξ) depending on a singular parameter ε → 0 with asymptotic properties measured by different scales. We prove, taking into account the asymptotic behavior for ε → 0, refined versions of estimates for classical pseudodifferential operators. We apply these estimates to nets of regularizations of exotic operators as well as operators with amplitudes of low regularity, providing a unified method for treating both classes. Further, we develop a full symbolic calculus for pseudo-differential operators acting on algebras of Colombeau generalized functions. As an application, we formulate a sufficient condition of hypoellipticity in this setting, which leads to regularity results for generalized pseudodifferential equations. | |
dc.description.department | Mathematics | |
dc.format | Text | |
dc.format.extent | 43 pages | |
dc.format.medium | 1 file (.pdf) | |
dc.identifier.citation | Garetto, C., Gramchev, T., & Oberguggenberger, M. (2005). Pseudodifferential operators with generalized symbols and regularity theory. Electronic Journal of Differential Equations, 2005(116), pp. 1-43. | |
dc.identifier.issn | 1072-6691 | |
dc.identifier.uri | https://hdl.handle.net/10877/13788 | |
dc.language.iso | en | |
dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
dc.rights | Attribution 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.source | Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
dc.subject | Pseudodifferential operators | |
dc.subject | Small parameter | |
dc.subject | Slow scale net | |
dc.subject | Algebras of generalized functions | |
dc.title | Pseudodifferential operators with generalized symbols and regularity theory | |
dc.type | Article |