Strong boundary values : independence of the defining function and spaces of test functions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 1, p. 13-31

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.

Classification:  46F15,  32A10,  32A40,  35G15,  35P20,  42C15,  58J32
@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},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {1},
     year = {2002},
     pages = {13-31},
     zbl = {1051.46026},
     mrnumber = {1994800},
     language = {en},
     url = {http://www.numdam.org/item/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, Serie 5, Volume 1 (2002) no. 1, pp. 13-31. http://www.numdam.org/item/ASNSP_2002_5_1_1_13_0/

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