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Compact linear operators of volterra type

Published online by Cambridge University Press:  24 October 2008

J. R. Ringrose
Affiliation:
St John's CollegeCambridge

Extract

1·1. Throughout this paper, all functions considered are assumed to be measurable, and an equation between two functions indicates equality almost everywhere. When the space Lp(a, b) is considered, the interval (a, b) may be finite, semi-infinite, or infinite.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

REFERENCES

(1)Banach, S.Théorie dea opérations linéaires (Warszawa, 1932).Google Scholar
(2)Dunford, N. and Pettis, B. J.Linear operations on summable functions. Trans. Amer. math Soc. 47 (1940), 323–92.CrossRefGoogle Scholar
(3)Gelfand, I. M., Raikov, D. A. and Shilov, G. E.Commutative normed rings. Progr. math. Sci., Moscow, n.s., 1, no. 2 (12) (1946), 48146 (in Russian).Google Scholar
(4)Hille, E.Functional analysis and semi-groups. Amer. Math Soc. Colloquium publications, 31 (1948).Google Scholar
(5)Hille, E. and Tamarkin, J. D.On the theory of linear integral equations. II. Ann. Math., Princeton (2), 35 (1934), 445–55.CrossRefGoogle Scholar
(6)Paley, R. E. A. C. and Wiener, N.Fourier transforms in the complex domain. Amer. Math. Soc. Colloquium Publications (1934), p. 60.Google Scholar
(7)Riesz, F.Untersuchungen über Systeme integrierbarer Functionen. Math. Ann. 69 (1910), 491–7.CrossRefGoogle Scholar
(8)Smithies, F.On the theory of linear integral equations. Proc. Camb. phil. Soc. 31 (1935), 7684.CrossRefGoogle Scholar
(9)Titchmarsh, E. C.Introduction to the theory of Fourier integrals (Oxford, 1937), p. 328.Google Scholar
(10)Zaanen, A. C.Integral transformations and their resolvents in Orlicz and Lebesgue spaces. Compos. math. 10 (1952), 5694.Google Scholar
(11)Zygmund, A.Trigonometrical Series (Warszawa, 1935).Google Scholar