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- W2003013617 abstract "We determine the limit, as $t to infty$, of the solution of the equation [{bf x}(t) + int_0^t {{bf A}(t - s){bf x}(s)ds = {bf x}_0 + t{bf k}} ] in Hilbert space. Here ${bf A}(t) = int _{ - infty }^infty A(t,lambda )d{bf E}_lambda $, where the spectral family ${{bf E}_lambda } $ corresponds to a fixed self adjoint linear operator ${bf L}$ and $A(t,lambda )$ has certain monotonicity properties as a function of t. The results generalize our earlier work on the special case ${bf A}(t) = A(t){bf L}$ with $A(t)$ scalar. The main new step is a continuity result for a related scalar equation depending on the parameter $lambda $." @default.
- W2003013617 created "2016-06-24" @default.
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- W2003013617 date "1974-11-01" @default.
- W2003013617 modified "2023-10-17" @default.
- W2003013617 title "A Linear Volterra Equation in Hilbert Space" @default.
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- W2003013617 doi "https://doi.org/10.1137/0505090" @default.
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