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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An abstract linear Volterra equation with a nonconvolution kernel


Author: T. Kiffe
Journal: Proc. Amer. Math. Soc. 82 (1981), 51-57
MSC: Primary 45N05; Secondary 45D05
MathSciNet review: 603600
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Abstract: This paper is concerned with the existence and uniqueness of solutions to the equation $ x(t) + \int_0^t {a(t,\tau )Ax(\tau )d\tau = f(t)} $ where $ A$ is an unbounded, positive, selfadjoint operator on a Hilbert space. A representation is given for the solution of this equation.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0603600-7
PII: S 0002-9939(1981)0603600-7
Article copyright: © Copyright 1981 American Mathematical Society