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absolutely and uniformly adjoint respectively aipi*i analytic Application to Integral ASSOCIATED INTEGRAL CONDITION auxiliary condition Bryn Mawr College charac coefficients with respect complete normed orthogonal continuous function continuous kernel converges absolutely discussion dtdx equations 17 exists a solution exists a symmetric expansion theorems expression 13 expression is equal finite norm follows Fourier coefficients Fredholm Determinant function p(s Hunter College I K(sx imaginary roots infinite number infinite series JgTn K(tx kernel L(sx LAURA GUGGENBUHL lemma matrix lap matrix tap normed orthogonal system obtain Pell Pell-Wheeler point spectrum poles positive definite properties real characteristic numbers Section series 2a series converge uniformly series in 24 single integral equation solutions of 21 sufficient condition symmetric matrix symmetrizable symmetrizing kernel system of equations system of functions teristic numbers Tg and Tn Tg exists theory ua(s Xfin