Some Fundamental Solutions Which Generalize Fresnel Integrals*

In an effort to generalize the space variable in the heat operator to complex space, we study the differential operators Ps­r­ tq­ mr­ zm, where ­r­ z is the usual complex operator ­r­ zs 1 ­r­ xyi­r­ y.. The primary tool for this study 2 is the Fourier transform. The main result is a formula for a fundamental solution in which Fresnel-like integrals arise.