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On a class of linear integro-differential equations

Published online by Cambridge University Press:  24 October 2008

H. R. Pitt
H. R. Pitt
Affiliation:
Queeen's UniversityBelfast
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Extract

This paper is a sequel to a previous one(1) with the same title which dealt with the general solution of equations of the type

We consider here the more general equation

where g(x) is a given function. We are interested particularly in the existence and uniqueness of solutions of the latter equation and show how these are related to the closure and completeness properties of sets of functions {xneωnx} derived from the kernels kr(y).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 43 , Issue 2 , April 1947 , pp. 153 - 163
Copyright
Copyright © Cambridge Philosophical Society 1947

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References

REFERENCES

(1)Pitt, H. R.On a class of integro-differential equations. Proc. Cambridge Phil. Soc. 40 (1944), 199–211.CrossRefGoogle Scholar
(2)Pitt, H. R.Mercerian theorems. Proc. Cambridge Phil. Soc. 34 (1938), 510–520.CrossRefGoogle Scholar
(3)Phragmén, E. and Lindelöf, E.Sur une extension d'un principe classique de l'analyse. Acta Math. 31 (1908), 381–406.CrossRefGoogle Scholar
(4)Wiener, N. and Pitt, H. R.On absolutely convergent Fourier-Stieltjes transforms. Duke Math. J. 4 (1938), 420–436.CrossRefGoogle Scholar
(5)Hardy, G. H., Littlewood, J. E. and Polya, G.Inequalities (Cambridge, 1934).Google Scholar
(6)Bochner, S.Vorlesungen über Fouriersche Integrale (Leipzig, 1932).Google Scholar