## A Family of Solutions of Certain Nonautonomous Differential Equations by Series of Exponential Functions |

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_ R2 Analytic Functions base of frequencies Cauchy's inequality CLEMSON coefficient and finite complex number components composite transformation consider the differential converges defined and analytic defined by 2.5 differential equation 3.3 ential Equations equation with odd EQUATIONS BY SERIES exists an invertible EXPONENTIAL FUNCTIONS family of periodic finite Fourier series Fourier-Taylor FUNCTIONS By T. G. Gelmand Golomb H. H. Suber iff Nm inequality 1.2 Kolmogorov l-nb Lemma Linear Differential Equations Math mp=n r mp=n n 2k n N el01 n n-vector n+v+2 NneI2k NONAUTONOMOUS DIFFERENTIAL EQUATIONS odd periodic coefficient period 2tt periodic solutions polydisk positive number Prepared under Grant prime p prime Proctor and H. H. proof quasi-periodic Ricatti equation right side satisfy SERIES OF EXPONENTIAL Small Divisors solution of 4.1 solution of equation solution with mean sufficiently small T. G. Proctor Theorem 2.1 uniformly and absolutely vector differential equation Wasow yŁymCp