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Semi-groups and differential equations

Published online by Cambridge University Press:  09 April 2009

J. D. Gray
J. D. Gray
Affiliation:
University of New South WalesKensington, N.S.W. Australia
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In this short note we shall apply the theory of semi-groups of operators, (cf: Hille and Phillips, [2]), to the problem of representing solutions of certain differential equations with non-constant coefficients. When the coefficients are constant, this representation reduces to the usual Laplace transform solution of the relevant equation.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 1-2 , August 1969 , pp. 173 - 176
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Dunford, N. and Schwartz, J. T., ‘Linear operators. Vol. I (Interscience, 1964, Second edition).Google Scholar
[2]Hille, E. and Phillips, R. S., ‘Functional analysis and semigroups’ (Amer. Math. Soc. Coll. XXXI, 1958).Google Scholar
[3]Szekeres, G. ‘Regular iteration of real and complex functions’. Acta Math. 100 (1958), 203–258.CrossRefGoogle Scholar