## An Application of the Laplace Transform to a Linear Volterra Equation |

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2kir 6+c-p oo A(iT a(t)cos Tt dt a(t)sin Tt dt abelian asymptotic behavior bounded c]dT c>0 and a(t Cauchy's theorem completes the proof continuous functions converges uniformly convexity Corollaries 3.l cosV6+c t define DOCTOR OF PHILOSOPHY e a(t)dt elT Wi function b(t give lim Halanay holds holomorphic implies integrand is continuous interval inversion formula iT)dT iV6+c J. J. Levin KENNETH HANNSGEN kernels satisfying Let a(t Levin and Nohel Levin's proof lim w(t lim Yj I T LINEAR VOLTERRA EQUATION Math nonincreasing nonnegative number t0 obtain oo oo positive integers proof of Lemma proof of Theorem proved Riemann-Lebesgue Theorem yields right-hand side rta(t sA(s satisfies H1 satisfies l.5 seguence set x0 show that a(t sinV6+c t skt0 solution of l.l Suppose a(t t-oo t0 n+l t0 Taking Laplace transforms Theorem 2(i transform of a(t U(iT University of Wisconsin V6+c W(iT W6+c