Abstract
with b2ac <0 whose coefficients are holomorphic functions of 6, Xj and r. We present a general method for the construction of explicit reflection formulae (analogous to the classical Schwarz reflection principle for harmonic functions) for solutions of (1.1) which vanish along a noncharacteristic analytic surface. These formulae (cf. (8.3) and (8.7)) have a domain of dependence consisting, in general, of a one-dimensional curve extending from the reflecting surface to a specific image point. In special cases, however, the domain of dependence may degenerate to just the image point. An interesting aspect of our technique is the use of fundamental solutions which have singularities not only along the real characteristic r = const. = t associated with (1.1) but also on certain complex characteristics as well. The simplest case of (1.1) is the heat equation
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