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The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.
@article{ASNSP_2002_5_1_1_13_0,
author = {Rosay, Jean-Pierre and Stout, Edgar Lee},
title = {Strong boundary values : independence of the defining function and spaces of test functions},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {13--31},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {1},
year = {2002},
mrnumber = {1994800},
zbl = {1051.46026},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_13_0/}
}
TY - JOUR AU - Rosay, Jean-Pierre AU - Stout, Edgar Lee TI - Strong boundary values : independence of the defining function and spaces of test functions JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2002 SP - 13 EP - 31 VL - 1 IS - 1 PB - Scuola normale superiore UR - http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_13_0/ LA - en ID - ASNSP_2002_5_1_1_13_0 ER -
%0 Journal Article %A Rosay, Jean-Pierre %A Stout, Edgar Lee %T Strong boundary values : independence of the defining function and spaces of test functions %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 13-31 %V 1 %N 1 %I Scuola normale superiore %U http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_13_0/ %G en %F ASNSP_2002_5_1_1_13_0
Rosay, Jean-Pierre; Stout, Edgar Lee. Strong boundary values : independence of the defining function and spaces of test functions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 13-31. http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_13_0/