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Monatshefte für Mathematik

, Volume 138, Issue 4, pp 307–318 | Cite as

Embedding Distributions in Algebras of Generalized Functions with Singularities

  • H. Vernaeve

Abstract.

 It is a known open question whether in Rosinger’s nowhere dense quotient algebra distributions can be embedded, ensuring consistency with partial derivatives. In this paper, we construct algebras of generalized functions with nowhere dense singularities similar to Rosinger’s algebra in which such an embedding of distributions is possible. Moreover, in some of the algebras, the embedding preserves the products of smooth functions. Further, we indicate that most of the properties of Rosinger’s algebra, in particular concerning the solvability of nonlinear PDEs, remain valid in the new algebras. Summarizing, we give a positive answer to the above-mentioned open question, if one allows a modification in the definition of the algebra that does not affect its basic properties.

46F30 26E35 
Distributions generalized functions nowhere dense singularities 

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Copyright information

© Springer-Verlag/Wien 2002

Authors and Affiliations

  • H. Vernaeve
    • 1
  1. 1.Ghent University, Gent, BelgiumBE

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