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Infinite Order Pseudo-Differential Operators

  • Stevan PilipovićEmail author
  • Bojan Prangoski
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We present a class of global pseudo-differential operators of infinite order which are intrinsically related to the spaces of tempered ultradistributions as well as the symbolic calculus these operators enjoy. We also give the notion of hypoellipticity in this setting and consider the complex powers of non-negative hypoelliptic pseudo-differential operators. Finally, we give the construction of the heat parametrix and present an application of these results to semigroups whose infinitesimal generators are square roots of non-negative operators having hypoelliptic Weyl symbols.

Keywords

Ultradistributions Infinite order pseudo-differential operators Hypoellipticity Complex powers Heat parametrix 

2010 Mathematics Subject Classification:

35S05 46F05 47D03 

Notes

Acknowledgements

The first author is supported by the Project 174024 of the Serbian Ministry. The second author was partially supported by the bilateral project “Microlocal analysis and applications” funded by the Macedonian and Serbian academies of sciences and arts.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsUniversity of Novi SadNovi SadSerbia
  2. 2.Department of Mathematics, Faculty of Mechanical EngineeringUniversity “Ss. Cyril and Methodius” in SkopjeSkopjeMacedonia

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