## Holomorphic Functions and Ordinary Differential EquationsThesis (M.A.)--University of California, Santa Cruz. |

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a(tQ b(tQ Banach space Cauchy formula Cauchy majorant Cauchy sequence Cauchy-Hadamard closed ball compact subset compact-open topology constant Continuous Polynomials converges uniformly cp is analytic cp(t defined denotes dmf(x domain e-approximate solution f converges f is bounded f is holomorphic f is Lipschitzian f(x+h f(Xg function f Hale Inequality Hence Hilbert space holomorphic function implies induction inf{r initial value problem integral interval Jacobi Identity Kellogg identity Let f Lie Algebra Lie Derivative Lie product lim sup linear Lipschitz condition lira locally Lipschitzian mapping matrix matrix-valued norm of f notation Note numbers open polydisc open set open subset order system Pm(x pointwise polarization formula power series proof Proposition radius of convergence Riemann definition Rudin seigel norm series converges series for f series of f sup f(x Taylor series uniform convergence variable Weierstrass definition x(tQ y(to y(tQ