The thesis describes almost periodic functions and their Fourier series Function defined on the real line is called almost periodic, if it can be uniformly approximated with any desired degree of accuracy by a finite linear combination of sine and cosine functions, or by a finite trigonometric polynomial. Almost periodic function is bounded, uniformly continuous and the sum and the product of almost periodic functions is also an almost periodic function. These properties are trivial for periodic functions but for almost periodic functions proving these properties might be very demanding. Almost periodic functions have also their generalized Fourier series. We thus have arrived at the basic questions: can every almost periodic function be represented with Fourier series and if a generalized Fourier series completely determines an almost periodic function. As with periodic functions, the idea of proving convergence of generalized Fourier series is to form partial Fourier sums and prove that these sums converge to the original function.
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