Pseudodifferential operators with generalized symbols and regularity theory

Simple item page
dc.contributor.authorGaretto, Claudia
dc.contributor.authorGramchev, Todor
dc.contributor.authorOberguggenberger, Michael
dc.date.accessioned2021-06-22T17:14:26Z
dc.date.available2021-06-22T17:14:26Z
dc.date.issued2005-10-21
dc.description.abstractWe 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.departmentMathematics
dc.formatText
dc.format.extent43 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationGaretto, C., Gramchev, T., & Oberguggenberger, M. (2005). Pseudodifferential operators with generalized symbols and regularity theory. <i>Electronic Journal of Differential Equations, 2005</i>(116), pp. 1-43.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/13788
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectPseudodifferential operators
dc.subjectSmall parameter
dc.subjectSlow scale net
dc.subjectAlgebras of generalized functions
dc.titlePseudodifferential operators with generalized symbols and regularity theory
dc.typeArticle

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
garetto.pdf
Size:
512 KB
Format:
Adobe Portable Document Format
Description:
Download

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
2.54 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Electronic Journal of Differential Equations