Geodesic
Functional Equations, Distributions and Approximate Identities
Canadian journal of mathematics, Tome 42 (1990) no. 4, pp. 696-708

Voir la notice de l'article provenant de la source Cambridge University Press

The subject of this paper is the use of the theory of Schwartz distributions and approximate identities in studying the functional equation The aj ’s and b are complex-valued functions defined on a neighbourhood, U, of 0 in R m , hj . U → R n with hj (0) = 0 and fj , g: Rn → C for 1 ≦ j ≦ N. In most of what follows the aj 's and hj 's are assumed smooth and may be thought of as given. The fj ‘s, b and g may be thought of as the unknowns. Typically we are concerned with locally integrable functions f 1, ... , fN such that, for each s in U, (1) holds for a.e. (almost every) x ∈ R n , in the sense of Lebesgue measure.
DOI : 10.4153/CJM-1990-036-1
Mots-clés : 39B20, 39B30, 39B40, 46F99 
Baker, John A. Functional Equations, Distributions and Approximate Identities. Canadian journal of mathematics, Tome 42 (1990) no. 4, pp. 696-708. doi: 10.4153/CJM-1990-036-1
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