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The overdetermined Cauchy problem for \(\omega \)-ultradifferentiable functions

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Abstract

In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of \(\omega \)-ultradifferentiable functions in the sense of Braun et al. (Results Math 17(3–4):207–237, 1990), for non-quasianalytic weight functions \(\omega \). We show that existence of solutions of the Cauchy problem is equivalent to the validity of a Phragmén–Lindelöf principle for entire and plurisubharmonic functions on some irreducible affine algebraic varieties.

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Acknowledgements

The authors are grateful to Prof. R. Meise for his helpful suggestions. The first author is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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

    Chiara Boiti & Elisabetta Gallucci

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  1. Chiara Boiti
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  2. Elisabetta Gallucci
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Correspondence to Chiara Boiti.

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Boiti, C., Gallucci, E. The overdetermined Cauchy problem for \(\omega \)-ultradifferentiable functions. manuscripta math. 155, 419–448 (2018). https://doi.org/10.1007/s00229-017-0939-2

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