In the framework of microlocal analysis, a boundary value morphism is defined for solutions to the regular-specializable system of analytic linear partial differential equations. This morphism can be regarded as a microlocal counterpart of the boundary value morphism for hyperfunction solutions due to Monteiro Fernandes, and the injectivity of this morphism (that is, the Holmgren type theorem) is proved. Moreover, under a kind of hyperbolicity condition, it is proved that this morphism is surjective (that is, the solvability).
Susumu YAMAZAKI. "Microlocal boundary value problem for regular-specializable systems." J. Math. Soc. Japan 56 (4) 1109 - 1129, October, 2004. https://doi.org/10.2969/jmsj/1190905451