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Multidimensional Volterra integral equations of convolution type

Part of: Linear function spaces and their duals Holomorphic functions of several complex variables Volterra integral equations Integral transforms, operational calculus

Published online by Cambridge University Press:  09 April 2009

P. G. Laird
P. G. Laird
Affiliation:
University of WollongongWollongong, N.S.W. 2500, Australia
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Abstract

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In this article, it is shown that the Volterra integral equation of convolution type w − w⊗g = f has a continuous solution w when f, g are continuous functions on Rx and ⊗ denotes a truncated convolution product. A similar result holds when f, g are entire functions of several complex variables. Also simple proofs are given to show when f, g are entire, f⊗g is entire, and, if f⊗g=0, then f = 0 or g = 0. Finally, the set of exponential polynomials and the set of all solutions to linear partial differential equations are considered in relation to this convolution product.

MSC classification

Secondary: 32A15: Entire functions 44A35: Convolution 45D05: Volterra integral equations 46E25: Rings and algebras of continuous, differentiable or analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 3 , May 1979 , pp. 305 - 312
Copyright
Copyright © Australian Mathematical Society 1979

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