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H-distributions with unbounded multipliers

  • Jelena Aleksić
  • Stevan Pilipović
  • Ivana Vojnović
Article

Abstract

We investigate H-distributions for sequences in the dual pairs of Bessel spaces, \((H^q_s , H^{p}_{-s}), s\in \mathbb {R}, q>1\) and \(q=p/(p-1),\) by the use of unbounded multipliers, with the finite regularity, as test functions. The results relating weak convergence, H-distributions and strong convergence are applied in the analysis of strong convergence for a sequence of approximated solutions to a class of differential equations \(P(x,D)u_n=f_n\), where P(xD) is a differential operator of order k with coefficients in the Schwartz class and \((f_n)\) is a strongly convergent sequence in an appropriate Bessel potential space.

Keywords

H-distributions Weak and strong convergence Bessel potential spaces Multipliers 

Mathematics Subject Classification

46F25 46F12 40A30 42B15 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • Jelena Aleksić
    • 1
  • Stevan Pilipović
    • 1
  • Ivana Vojnović
    • 1
  1. 1.Department of Mathematics and Informatics, Faculty of SciencesUniversity of Novi SadNovi SadSerbia

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