Almost periodic functions in finite-dimensional space with the spectrum in a cone
S. Favorov, O. Udodova
Abstract
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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