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arXiv · 1701.07691

Periodic distributions and periodic elements in modulation spaces

Joachim Toft·Elmira Nabizadeh
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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. If $q\in [1,\infty )$, $ω$ is a suitable weight and $(\maclE _0^E)'$ is the set of all $E$-periodic elements, then we prove that the dual of $M^{\infty ,q}_{(ω)}\cap (\maclE _0^E)'$ equals $M^{\infty ,q'}_{(1/ω)}\cap (\maclE _0^E)'$ by suitable extensions of Bessel's identity.

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Joachim Toft, Elmira Nabizadeh. 2017-06-11. Periodic distributions and periodic elements in modulation spaces. https://arxiv.org/abs/1701.07691

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