Evolution system approximations of solutions to closed linear operator equations

Purdom, Seaton D.

doi:10.1090/S0002-9947-1976-0420331-X

Evolution system approximations of solutions to closed linear operator equations
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by Seaton D. Purdom

Trans. Amer. Math. Soc. 215 (1976), 63-79

DOI: https://doi.org/10.1090/S0002-9947-1976-0420331-X

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Abstract:

With S a linearly ordered set with the least upper bound property, with g a nonincreasing real-valued function on S, and with A a densely defined dissipative linear operator, an evolution system M is developed to solve the modified Stieljes integral equation $M(s,t)x = x + A((L)\smallint _S^t dgM( \cdot ,t)x)$. An affine version of this equation is also considered. Under the hypothesis that the evolution system associated with the linear equation is strongly (resp. weakly) asymptotically convergent, an evolution system is used to approximate strongly (resp. weakly) solutions to the closed operator equation $Ay = - z$.

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