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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 196, Issue 6, pp 2239–2251 | Cite as

Convolvability and regularization of distributions

  • C. Bargetz
  • E. A. Nigsch
  • N. Ortner
Article

Abstract

We apply L. Schwartz’ theory of vector-valued distributions in order to simplify, unify and generalize statements about convolvability of distributions, their regularization properties and topological properties of sets of distributions. The proofs rely on propositions on the multiplication of vector-valued distributions and on the characterization of the spaces \(\mathcal {O}_{M}(E,F)\) and \(\mathcal {O}_{C}'(E,F)\) of multipliers and convolutors for distribution spaces E and F.

Keywords

Vector-valued distributions Convolvability Convolution Regularization Multiplication 

Mathematics Subject Classification

Primary 46F10 Secondary 46F05 

Notes

Acknowledgements

E.A. Nigsch was supported by Grant P26859-N25 of the Austrian Science Fund (FWF).

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institut für MathematikUniversität InnsbruckInnsbruckAustria
  2. 2.Wolfgang Pauli InstituteWienAustria

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