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Global Gevrey vectors

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Abstract

In this paper, we introduce the notion of global \(L^q\) Gevrey vectors and investigate the regularity of such vectors in global and microglobal settings when \(q=2\). We characterize the vectors in terms of the FBI transform and prove global and microglobal versions of the Kotake–Narasimhan Theorem. Our techniques are new because our results are written in terms of the FBI transform and not the Fourier transform. Additionally, the microglobal Kotake–Narasimhan Theorem provides a refinement of an earlier result by Hoepfner and Raich relating the microglobal wavefront sets of the ultradistributions u and Pu when P is a constant coefficient differential operator.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brazil

    G. Hoepfner

  2. Department of Mathematical Sciences, SCEN 327, 1 University of Arkansas, Fayetteville, AR, 72701, USA

    A. Raich

  3. Departamento de Ciências Exatas, Biológicas e da Terra, Universidade Federal Fluminense, Niterói, RJ, 24220-900, Brazil

    P. Rampazo

Authors
  1. G. Hoepfner
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  2. A. Raich
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  3. P. Rampazo
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All authors contributed equally to the research, writing, and reviewing of this article.

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Correspondence to A. Raich.

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Conflict of interest

We declare that we do not have any conflict of interests or competing interests. Additionally, data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

Additional information

G. Hoepfner was partially supported by FAPESP (2018/14316-3 and 2019/04995-3) and CNPq (308826/2018-3). A. Raich was partially supported by a Grant from the Simons Foundation (707123, ASR). P. Rampazo was partially supported by CAPES (1492101).

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Hoepfner, G., Raich, A. & Rampazo, P. Global Gevrey vectors. Complex Anal Synerg 9, 11 (2023). https://doi.org/10.1007/s40627-023-00120-y

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