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On Spectral Synthesis for Contractive p-Norms and Besov Spaces

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Abstract

We prove that spectral synthesis is possible for a general function space F p with a contractive p-norm, namely, any quasi-continuous function in F p vanishing q.e. outside an open set G can be approximated in this norm by continuous functions in F p with compact support in G. The result is applied to contractive Besov spaces over d-sets in R N and censored stable processes over N-sets.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Engineering, Kansai University, Suita, Osaka, Japan, 564-8680 (e-mail

    Masatoshi Fukushima

  2. Department of Management Science, Kobe University of Commerce, Nishi, Kobe, Japan, 651-2197 (e-mail

    Toshihiro Uemura

Authors
  1. Masatoshi Fukushima
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  2. Toshihiro Uemura
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Fukushima, M., Uemura, T. On Spectral Synthesis for Contractive p-Norms and Besov Spaces. Potential Analysis 20, 195–206 (2004). https://doi.org/10.1023/A:1026365221549

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  • DOI: https://doi.org/10.1023/A:1026365221549

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