Geodesic
Order and Schwartz distributions†
Glasgow mathematical journal, Tome 18 (1977) no. 1, pp. 25-33

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

The space of Schwartz distributions on the unit circle Г in the plane is topologically a considerable generalization of the space of regular, finite Borel measures on Г. However, the order structure of is usually taken to be the same as that of : there are no “positive” distributions which are not measures. This perhaps warrants consideration, since the order structure of generates its topology. In this paper we construct a system of order structures for which is a more natural complement in the intermediate stages to the topology of and which provides an interpretation of with its Schwartz topology as a quotient of a generalized base norm space V′. Where denotes the space of continuous functions on Г with its supremum norm topology, V′ is the dual of . The space contains the infinitely differentiable functions on Г with their usual topology, and (via the pointwise ordering on ) in its product ordering is realized as a generalized order unit space. Some consequences for harmonic functions are discussed. 
Feldman, W. A.; Porter, J. F. Order and Schwartz distributions†. Glasgow mathematical journal, Tome 18 (1977) no. 1, pp. 25-33. doi: 10.1017/S0017089500002998
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