Geodesic
The expansion of continuous functions in series of integrals of orthonormal functions
Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 29-38

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

This paper deals with the following problem: Can an arbitrary continuous function on [0, 1], which vanishes at the origin, be represented in some sense as a series of constant multiples of indefinite integrals of a complete orthonormal set of functions on [0,1]? Four contexts in which this problem arises naturally will be given in the introduction and the remainder of the paper will be devoted to giving a partial answer to the specific problem formulated in one of these contexts. 
Finlayson, H. C. The expansion of continuous functions in series of integrals of orthonormal functions. Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 29-38. doi: 10.1017/S0017089500001336
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