Boundary Values in Ultradistribution Spaces Related to Extended Gevrey Regularity

Stevan Pilipović, Nenad Teofanov and Filip Tomić
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Stevan Pilipović: Faculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia
Nenad Teofanov: Faculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia
Filip Tomić: Faculty of Technical Sciences, Department of Fundamental Sciences, University of Novi Sad, 21000 Novi Sad, Serbia

Mathematics, 2020, vol. 9, issue 1, 1-14

Abstract: 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.

Keywords: ultradifferentiable functions; ultradistributions; extended Gevrey regularity; boundary values of analytic functions; wave front sets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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