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A characterization of the wave front set defined by the iterates of an operator with constant coefficients

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We characterize the wave front set \(\mathrm{WF}^P_*(u)\) with respect to the iterates of a linear partial differential operator with constant coefficients of a classical distribution \(u\in \mathcal {D}'(\Omega )\), \(\Omega \) an open subset in \(\mathbb R^n\). We use recent Paley–Wiener theorems for generalized ultradifferentiable classes in the sense of Braun, Meise and Taylor. We also give several examples and applications to the regularity of operators with variable coefficients and constant strength. Finally, we construct a distribution with prescribed wave front set of this type.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Ferrara, Via Machiavelli n. 30, 44121, Ferrara, Italy

    Chiara Boiti

  2. Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, Camino de Vera, s/n, E-46071, Valencia, Spain

    David Jornet

Authors
  1. Chiara Boiti
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  2. David Jornet
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Correspondence to David Jornet.

Additional information

The authors were partially supported by FAR2011 (Università di Ferrara), “Fondi per le necessità di base della ricerca” 2012 and 2013 (Università di Ferrara) and the INDAM-GNAMPA Project 2014 “Equazioni Differenziali a Derivate Parziali di Evoluzione e Stocastiche” The research of the second author was partially supported by MINECO of Spain, Project MTM2013-43540-P.

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Boiti, C., Jornet, D. A characterization of the wave front set defined by the iterates of an operator with constant coefficients. RACSAM 111, 891–919 (2017). https://doi.org/10.1007/s13398-016-0329-8

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  • DOI: https://doi.org/10.1007/s13398-016-0329-8

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