Boundary Values in Ultradistribution Spaces Related to Extended Gevrey Regularity

• Main Authors: Stevan Pilipović, Nenad Teofanov, Filip Tomić
• Format: Article
• Language: English
• Published: MDPI AG 2021-12-01
• Series: Mathematics
• Subjects: ultradifferentiable functions; ultradistributions; extended Gevrey regularity; boundary values of analytic functions; wave front sets
• Online Access: https://www.mdpi.com/2227-7390/9/1/7

Following the well-known theory of Beurling and Roumieu ultradistributions, we investigate new spaces of ultradistributions as dual spaces of test functions which correspond to associated functions of logarithmic-type growth at infinity. In the given framework we prove that boundary values of analytic functions with the corresponding logarithmic growth rate towards the real domain are ultradistributions. The essential condition for that purpose, known as stability under ultradifferential operators in the classical ultradistribution theory, is replaced by a weaker condition, in which the growth properties are controlled by an additional parameter. For that reason, new techniques were used in the proofs. As an application, we discuss the corresponding wave front sets.