Almost periodic functions in finite-dimensional space with the spectrum in a cone

Mathematics – Complex Variables

Scientific paper

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Scientific paper

An almost periodic function in finite-dimensional space extends to a
holomorphic bounded function in a tube domain with a cone in the base if and
only if the spectrum belongs to the conjugate cone. Also, an almost periodic
function in finite-dimensional space has the bounded spectrum if and only if it
extends to an entire function of exponential type.

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