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An Abstract Linear Volterra Equation with a Nonconvolution Kernel
Proceedings of the American Mathematical Society
Vol. 82, No. 1 (May, 1981), pp. 51-57
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2044315
Page Count: 7
You can always find the topics here!Topics: Volterra equations, Hilbert spaces, Uniqueness, Differential equations, Mathematics
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This paper is concerned with the existence and uniqueness of solutions to the equation $x(t) + \int^t_0 a(t, \tau)Ax(\tau) d\tau = f(t)$ where $A$ is an unbounded, positive, selfadjoint operator on a Hilbert space. A representation is given for the solution of this equation.
Proceedings of the American Mathematical Society © 1981 American Mathematical Society