Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Cappiello, Marco; Schulz, René
• Is Part Of: Complex variables and elliptic equations. Volume 61:Issue 4(2016)
• Page Start: 538
• Page End: 561
• Publication Date: 2016-04-02
• Subjects: Gelfand–Shilov spaces -- global wave front sets -- Bargmann transform -- localization operators -- tempered ultradistributions; 35A18 -- 35A22 -- 35A27 -- 46F05; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2015.1106481
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : We introduce a global wave front set suitable for the analysis of tempered ultradistributions of quasi-analytic Gelfand–Shilov type. We study the transformation properties of the wave front set and use them to give microlocal existence results for pullbacks and products. We further study quasi-analytic microlocality for classes of localization and ultradifferential operators, and prove microellipticity for differential operators with polynomial coefficients.