no. 1
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

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 
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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. https://www.numdam.org/item/ASNSP_2002_5_1_1_13_0/

[1] N. Aronszajn - T. M. Creese - L. J. Lipkin, “Polyharmonic Functions”, The Clarendon Press Oxford University Press, New York, 1983. Notes taken by Eberhard Gerlach, Oxford Science Publications. | Zbl | MR

[2] I. Chavel, “Eigenvalues in Riemannian Geometry”, Academic Press Inc., Orlando, 1984, including a chapter by Burton Randol, with an appendix by Jozef Dodziuk. | Zbl | MR

[3] G. B. Folland, “Introduction to Partial Differential Equations, 2nd. ed.”, Princeton University Press, Princeton, 1995. | Zbl | MR

[4] L. V. Hörmander, “Linear Partial Differential Operators”, volume 116 of Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1964.

[5] L. V. Hörmander, “The Analysis of Linear Partial Differential Operators”, volume 275 of Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1985. | Zbl

[6] J.-P. Rosay - E. L. Stout, “Strong Boundary Values, Analytic Functionals, and Nonlinear Paley-Wiener Theory”, Memoirs of the American Mathematical Society, American Mathematical Society, Providence, Vol. 153, n. 725, 2001. | Zbl | MR

[7] W. Rudin, “Functional Analysis”, McGraw-Hill, New York, 1991. | Zbl | MR