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On the structure of certain ultradistributions

Sobre la estructura de ciertas ultradistribuciones

Abstract

Let Ω be a nonempty open subset of the k-dimensional euclidean space ℝk. In this paper we show that, if S is an ultradistribution in Ω, belonging to a class of Roumieu type stable under differential operators, then there is a family \( f_\alpha ,\alpha \in _0^k \) , of elements of \( {\cal L}_{loc}^\infty (\Omega ) \) such that S is represented in the form \( \Sigma _{\alpha \in _0^k } D^\alpha f_\alpha \) . Some other results on the structure of certain ultradistributions of Roumieu type are also given.

Resumen

Sea Ω un subconjunto abierto no vacío del espacio euclídeo k-dimensional ℝk. En este trabajo demostramos que si S es una ultradistribución en Ω, perteneciente a una clase de tipo Roumieu estable bajo operadores diferenciales, entonces existe una familia \( f_\alpha ,\alpha \in _0^k \) , de elementos de \( {\cal L}_{loc}^\infty (\Omega ) \) tal que S se representa en la forma \( \Sigma _{\alpha \in _0^k } D^\alpha f_\alpha \) . También se dan otros resultados sobre la estructura de ciertas ultradistribuciones de tipo Roumieu.

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References

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Author information

Correspondence to Manuel Valdivia.

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Cite this article

Valdivia, M. On the structure of certain ultradistributions. Rev. R. Acad. Cien. Serie A. Mat. 103, 17–48 (2009). https://doi.org/10.1007/BF03191831

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Keywords

  • Roumieu class
  • ultradifferentiable class
  • ultradistributions

Mathematics Subject Classifications

  • 46F05