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1995 International Press algebraic Allen-Cahn equation Anal analytic Applications of Analysis approximation arbitrary Askey assume asymptotic expansions Banach space Bessel functions boundary conditions bounded Cahn-Hilliard equation coefficients compute consider constant continued fractions convergence corresponding CZDS Darboux transformations defined Definition denote derive differential equations discrete DTTL eigenfunctions eigenvalue entire function estimate example exists exponentially finite follows formula given Hence hyperasymptotic inequality infinite integral equation internal layer International Press ISSN interpolation interval kernel lattice Laurent polynomials Lemma limit linear Math Mathematics Subject Classification measure Methods and Applications multiplier sequence Navier-Stokes equations nonlinear nonnegative notation obtain operator orthogonal polynomials paper parameter Phys poles positive zero potentials problem proof of Theorem Proposition respectively s)ds saddle point sampling theorem satisfy singularity space Stieltjes Stieltjes transforms Theorem 2.1 uniformly unique solution values Volterra Zak transform