Abstract
The purpose of the present paper is to construct approximations of the Sobolev spacesH m(R n) using the translates ofp functions which satisfy a property of partition of unity.
These approximations generalise these constructed in an earlier paper [5], which are here obtained as a special case forp=1; they also achieve the same accuracy.
They involvep arbitrary functions ofH m (R n) which can be considered asp degrees of freedom. This fact could be of interest when dealing with the approximate matrices obtained by discretisation of boundary value problems for partial differential equations for the purpose of minimizing their spectral radius or lowering their condition number.
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Di Guglielmo, F. Méthode des éléments finis: Une famille d’approximations des espaces de sobolev par les translatés dep fonctions. Calcolo 7, 185–233 (1970). https://doi.org/10.1007/BF02575560
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DOI: https://doi.org/10.1007/BF02575560