Abstract
where II, v > 0, and rV(r) is an entire function of T = +(x2 + y2)l12. We shall introduce an integral operator S2,,[f] which relates analytic functions of one complex variable, f(z), in a one-to-one manner to regular solutions of (1.1). We shall develop necessary and sufficient conditions for a solution I/J(X, y) to be singular at a point (x0, y”), in terms of its associated analytic function. Using this result we give criteria analogous to the Cauchy, Hadamard, and Mandelbrojt [8,29] results concerning the location of singularities of solutions represented as infinite series of the form
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