Abstract:
We consider slowly varying and periodic at infinity multivariable functions in Banach space. We introduce the notion of Fourier series of periodic at infinity function, study the properties of Fourier series and their convergence. Basic results are derived with the use of isometric representations theory.
Key words:Banach space, Banach algebra, slowly varying at infinity functions, periodic at infinity functions, Fourier series, modulus of continuity.
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