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This paper and its successor, 10, extend to boundary value problems the analysis of the powers of an elliptic operator given in 9. (Similar methods are applied in 3, 5, and 6 for the case without boundary; 5a announces boundary results.) Although 9 treated general elliptic pseudo-differential operators on compact manifolds, we restrict ourselves here to differential operators, except in the final section, where we correct some (fortunately inconsequential) errors in the proof given in 9. We consider a q X q system A = > aaDa of Cdifferential operators
R. Seeley (Wed,) studied this question.