Abstract
are defined in D. In this connection, D, is a generic symbol for any of the partial derivatives of order t,. It will be assumed that f C L2 in D. Throughout this work any statement to the effect that a complex valued function q c L2 in a. domain R will be in the sense that q is measurable and that lq 12 is integrable over R. More precise hypotheses will be introduced in the sequel (see hypothesis (2.13)). The type of problems, relating to (1.1), which we shall study are suggested, in part, by T. Carleman's' investigation of a Schrddinger wave equation, which in the sequel will be referred to as (C). Carleman utilizes for this purpose the methods of his theory of singular integral equations2 in the sequel referred to as (C1). The case treated in (C) is
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