Periodic distributions and periodic elements in modulation spaces

2017/01/26 by Toft, Joachim, Nabizadeh, Elmira
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1701.07691

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 (\maclE ₀^E)' is the set of all E-periodic elements, then we prove that the dual of M^{∞ ,q}_(ω)∩ (\maclE ₀^E)' equals M^{∞ ,q'}_(1/ω)∩ (\maclE ₀^E)' by suitable extensions of Bessel's identity.

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