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arXiv · 1801.06803

Nonlinear operations on a class of modulation spaces

Tomoya Kato·Mitsuru Sugimoto·Naohito Tomita
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Abstract

We discuss when the nonlinear operation $f\mapsto F(f)$ maps the modulation space $M^{p,q}_s(\mathbb{R}^n)$ ($1 \leq p,q \leq \infty$) to the same space again. It is known that $M^{p,q}_s(\mathbb{R}^n)$ is a multiplication algebra when $s > n-n/q$, hence it is true for this space if $F$ is entire. We claim that it is still true for non-analytic $F$ when $q\geq4/3$.

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Tomoya Kato, Mitsuru Sugimoto, Naohito Tomita. 2018-01-21. Nonlinear operations on a class of modulation spaces. https://arxiv.org/abs/1801.06803

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