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Periodic distributions and periodic elements in modulation spaces

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Abstract We characterize periodic elements in Gevrey classes, Gelfand–Shilov distribution spaces and modulation spaces, in terms of estimates of involved Fourier coefficients, and by estimates of their short-time Fourier transforms.… Click to show full abstract

Abstract We characterize periodic elements in Gevrey classes, Gelfand–Shilov distribution spaces and modulation spaces, in terms of estimates of involved Fourier coefficients, and by estimates of their short-time Fourier transforms. If q ∈ [ 1 , ∞ ) , ω is a suitable weight and ( E 0 E ) ′ is the set of all E-periodic elements, then we prove that the dual of M ( ω ) ∞ , q ∩ ( E 0 E ) ′ equals M ( 1 / ω ) ∞ , q ′ ∩ ( E 0 E ) ′ by suitable extensions of Bessel's identity.

Keywords: modulation spaces; periodic distributions; periodic elements; elements modulation; distributions periodic

Journal Title: Advances in Mathematics
Year Published: 2017

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