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Almost Periodic Functions
The space APC
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a c a Acad Akad Amer AP(E Appl asymptotically stable Banach spaces Bochner Bohr bounded solution boundedness compact sets compact subsets condition constant converges uniformly Corollary cp(t cp(t+T defined Definition eigenvalues exists uniformly exp(f exponential dichotomy exponents f e AP(C f exists f uniformly f x,t F(x+T fact finite Floquet Theory fourier series fundamental solution given hull implies inequality integral interval kinematically similar Lemma linear differential equations linear systems ll.l Math matrix mod(f Nauk SSSR nonlinear norm Note ordinary differential equations periodic coefficients periodic functions periodic solutions periodic systems pointwise presque-periodiques Proc Proof quasi-periodic real numbers relatively dense Russian satisfies an exponential scalar equation sequence standard hypothesis Suppose Theorem 5.8 trigonometric polynomials u.a.p. family uniform convergence uniformly asymptotically stable uniformly continuous uniformly on compact unique solutions vector zero