We consider well-posedness of microhyperbolic Cauchy problems in the category of microlocal ultradistributions. For this purpose, we discuss about the expression of microdifferential operators, and define their irregularities. This enables us to give a general theory about the well-posedness.
Keisuke UCHIKOSHI. "Irregularities of microhyperbolic operators." J. Math. Soc. Japan 58 (2) 453 - 484, April, 2006. https://doi.org/10.2969/jmsj/1149166784