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

S. Favorov·O. Udodova
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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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S. Favorov, O. Udodova. 2007-01-28. Almost periodic functions in finite-dimensional space with the spectrum in a cone. https://arxiv.org/abs/math/0701820

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