Unique continuation of microlocally analytic functions and their structure

Abstract

We study a unique continuation property of microlocally analytic functions. This property depends on the regularity of the functions. In this article, we mainly discuss the unique continuation property of the microlocally analytic quasi-analytic ultradistributions and hyperfunctions, whose relation with their structure is also discussed.

Keywords:

• unique continuation
• structure theorem
• ultradistributions
• hyperfunctions
• microlocal analyticity

AMS Subject Classifications::

• 35A02
• 32A45
• 46F15
• 35A27

Acknowledgements

Dedicated to Professor Akira Kaneko in honor of his retirement. This work was supported in part by JSPS Grant-in-Aid for Scientific Research (C) 22540214.